Benchmarking Tabular Reinforcement Studying Algorithms

Empowering LLMs to Assume Deeper by Erasing Ideas

ACP: The Web Protocol for AI Brokers

posts, we explored Half I of the seminal guide Reinforcement Studying by Sutton and Barto [1] (*). In that part, we delved into the three basic methods underlying almost each trendy Reinforcement Studying (RL) algorithm: Dynamic Programming (DP), Monte Carlo strategies (MC), and Temporal Distinction Studying (TD). We not solely mentioned algorithms from every area in depth but additionally applied every one in Python.

Half I of the guide focuses on tabular answer strategies — approaches suited to issues sufficiently small to be represented in desk kind. As an example, with Q-learning, we will compute and retailer an entire Q-table containing each attainable state-action pair. In distinction, Half II of Sutton’s guide tackles approximate answer strategies. When state and motion areas change into too giant — and even infinite — we should generalize. Contemplate the problem of taking part in Atari video games: the state area is just too huge to mannequin exhaustively. As an alternative, deep neural networks are used to compress the state right into a latent vector, which then serves as the premise for an approximated worth perform [2].

Whereas we’ll enterprise into Half II in upcoming posts, I’m excited to announce a brand new collection: we’ll benchmark all of the algorithms launched in Half I towards each other. This submit serves each as a abstract and an introduction to our benchmarking framework. We’ll consider every algorithm primarily based on how shortly and successfully it may well clear up more and more bigger Gridworld environments. In future posts, we plan to increase our experiments to tougher eventualities, comparable to two-player video games, the place the variations between these strategies shall be much more obvious.

Summarized, on this submit, we’ll:

Introduce the benchmark job and talk about our comparability standards.
Present a chapter-by-chapter abstract of the strategies launched in Sutton’s guide together with preliminary benchmarking outcomes.
Establish the best-performing strategies from every group and deploy them in a larger-scale benchmarking experiment.

Desk of Contents

Introducing the Benchmark Process and Experiment Planning

On this submit we’ll work with the Gymnasium [3] surroundings “Gridworld”. It’s basically a maze-finding job, during which the agent has to get from the top-left nook of the maze to the bottom-right tile (the current) — with out falling into any of the icy lakes:

The state area is a quantity between 0 and N — 1, the place N is the maximal variety of tiles (16 in our case). There are 4 actions the agent can execute in each step: going left, proper, up or down. Reaching the objective yields reward 1, falling into the lake ends the episode with none reward.

The good factor about this surroundings is that one can generate random worlds of arbitrary dimension. Thus, what we’ll do with all strategies, is plot the variety of steps / updates wanted to unravel the surroundings versus the surroundings dimension. In actual fact, Sutton does this in some elements of the guide, too, so we will seek advice from that.

Preliminaries

I’d like to begin with some basic notes — hoping these will information you thru my thought course of.

It isn’t simple to check algorithms in a “honest” approach. When implementing the algorithms I primarily seemed for correctness, but additionally simplicity — that’s, I needed readers to simply have the ability to join the Python code with pseudocode from Sutton’s guide. For “actual” use circumstances, one would absolutely optimize the code extra, and in addition use a big array of tips frequent in RL, comparable to utilizing decaying exploration, optimistic initialization, studying fee tuning, and extra. Additional, one would take nice care to tune the hyperparameters of the deployed algorithm.

Utilized RL Methods

As a result of giant variety of algorithms underneath investigation, I can’t do that right here. As an alternative, I recognized two necessary mechanisms, and measured their effectiveness on an algorithm recognized to work fairly properly: Q-learning. These are:

Intermediate rewards: as an alternative of solely rewarding the agent for reaching the objective, we reward it for progress alongside the maze. We quantify this by the (normalized) distinction in x and y coordinates between present and former state. This makes use of the truth that the objective in every Gridworld surroundings is at all times on the backside proper, and thus greater x / y coordinates often are higher (though one may nonetheless get “caught”, in case an icy lake is between the agent and the objective). Since this distinction is normalized by the variety of states, its contribution is small, s.t. it doesn’t overshadow the reward of reaching the objective.
Decaying exploration: all through this submit collection, the exploration-exploration dilemma got here up often. It describes the trade-off of exploiting states / actions already recognized to be good, and exploring much less explored states — probably discovering even higher options, on the danger of losing time in much less optimum areas. One frequent approach addressing that is to decay exploration: beginning with a excessive quantity of exploration early, and slowly decaying this right down to decrease ranges. We do that by linearly decaying ε from 1 (100% random exploration) to 0.05 over 1000 steps.

Let’s take a look at how Q-learning performs with these methods:

As we will see, within the baseline setup the variety of steps wanted shortly grows, and reaches the maximal variety of allowed steps (100.000 ) — which means the algorithm didn’t clear up the surroundings within the allotted variety of steps. Additionally decaying ε alone didn’t contribute a lot. Nevertheless, including intermediate rewards proved to be extraordinarily efficient — and the mix of this and decaying ε carried out finest.

Thus, for many strategies to come back we begin with the “naïve” surroundings, the baseline implementation. Later we present outcomes for the “improved” surroundings consisting of intermediate rewards and decaying exploration.

Comparability Standards

As was seen within the earlier part I selected the variety of steps wanted till the discovered coverage solves the Gridworld surroundings because the default approach of evaluating strategies. This appears a bit extra honest than simply measuring elapsed time, since time depends upon the concrete implementation (much like the idea of Large O notation)— and, as talked about above, I didn’t optimize for velocity. Nevertheless, it is very important observe that additionally steps could be deceptive, as e.g. one step in DP strategies incorporates a loop over all states, whereas one step in MC and TD strategies is the era in a single episode (really for TD strategies we often rely one step as one worth replace, i.e. an episode era consists of a number of steps — nevertheless I made this extra corresponding to MC strategies on objective). Because of this we additionally present elapsed time generally.

Experiment Construction

To scale back the variance, for every Gridworld dimension we run every technique thrice, after which save the bottom variety of steps wanted.

The code required to run all following benchmarking could be discovered on GitHub.

Recap and Benchmarking of All Algorithms

With the basics out of the way in which, let’s correctly get began. On this part we’ll recap all launched algorithms from Half I of Sutton’s guide. Additional, we’ll benchmark them towards one another on the beforehand launched Gridworld job.

Dynamic Programming

We begin with Chapter 4 of Sutton’s guide, describing strategies from DP. These could be utilized to all kinds of issues, at all times constructing on the precept of iteratively constructing bigger options from smaller subproblems. Within the context of RL, DP strategies preserve a Q-table which is stuffed out incrementally. For this, we require a mannequin of the surroundings, after which, utilizing this mannequin, replace the anticipated worth of states or state-action pairs relying on the attainable successor states. Sutton introduces two strategies we picked up in our corresponding submit: coverage and worth iteration.

Let’s begin with coverage iteration. This consists of two interleaved steps, specifically coverage analysis and coverage enchancment. Coverage analysis makes use of DP to — because the title says — consider the present coverage: we incrementally replace the state estimates through the use of the mannequin and coverage. Subsequent comes coverage enchancment, which employs a basic idea of RL: in keeping with the coverage enchancment theorem, any coverage will get higher when altering the expected motion in a single state to a greater motion. Following this, we assemble the brand new coverage from the Q-table in grasping trend. That is repeated, till the coverage has converged.

The corresponding pseudocode seems to be as follows:

Let’s come to worth iteration. That is similar to coverage iteration, however with a easy, but essential modification: in each loop, just one step of coverage analysis is run. It may be proven that this nonetheless converges to the optimum coverage, and total does so quicker than coverage iteration:

For extra particulars, right here’s my corresponding submit about DP strategies.

Outcomes

Now it’s time to see what these first two algorithms are actually fabricated from. We run the experiment sketched above, and get the next plot:

Each strategies are in a position to clear up all created Gridworld sizes within the minimal variety of steps, 100. Shocking? Properly, this really exhibits each a energy and in addition to a weak point of DP strategies, as concurrently of our methodology: DP strategies are “thorough”, they require an entire mannequin of the world, after which iterate over all states — yielding a very good answer with just some passes over all states. Nevertheless, which means that all states have to be estimated until convergence — regardless that a few of them could be a lot much less fascinating — and this scales fairly badly with the surroundings dimension. In actual fact, one measured step right here incorporates a full run over all states — indicating that for these strategies time is a greater measure.

For this, we get the next graph:

Now, we will see enhance in compute wanted w.r.t. to the variety of states. And, we will additionally see that, as claimed, worth iteration converges a lot quicker, and scales a lot better. Observe that the x-axis labels denote n, with the Gridworld having a dimension of n x n.

Monte Carlo Strategies

Subsequent in our submit collection on RL we lined MC strategies. These can study from expertise alone, i.e. one can run them in any sort of surroundings, with out having a mannequin of it — which is a surprising realization, and really helpful: usually, we don’t have this mannequin, different instances, it will be too advanced and impractical to make use of. Contemplate the sport of Blackjack: whereas we will actually mannequin all attainable outcomes and corresponding chances, it’s a very tedious job — and studying to play by simply doing that may be a very tempting thought. Because of not utilizing a mannequin, MC strategies are unbiased — however on the draw back their expectation has a excessive variance.

One subject when implementing these strategies is ensuring that every one state-action pairs are repeatedly visited, and thus up to date. Because of not having a mannequin, we can’t merely iterate over all attainable combos (evaluate e.g. DP strategies), however (in a approach) randomly discover the surroundings. If attributable to this we missed some states solely, we’d free theoretical convergence ensures, which might translate into observe.

A method of satisfying that is the exploring begins assumption (ES): we begin every episode in a random state and select the primary motion randomly, too. Other than that, MC strategies could be applied quite merely: we merely play out full episodes, and set the anticipated worth of state-action pairs to the typical obtained reward.

MC with ES seems to be as follows:

To take away the belief of ES, we will resort to 2 lessons of algorithms: on- and off-policy strategies. Let’s begin with the on-policy one.

That is really not too completely different from the ES algorithm, we merely use an ε-greedy coverage for producing episodes. That’s, we take away the belief of ES and use a “tender” as an alternative of a “laborious” coverage for producing episodes: the used coverage in each iteration is just not totally grasping, however ε-greedy — which ensures that within the restrict we see all attainable state-action pairs:

Off-policy strategies comply with the concept of splitting exploration and studying in two insurance policies. We preserve a coverage π, which we wish to optimize, and a habits coverage, b.

Nevertheless, we will’t merely use b in every single place in our algorithm. When producing an episode and computing returns, we acquire:

I.e., the ensuing worth is the expected worth of b, not π.

That is the place significance sampling is available in. We are able to repair this expectation with the best ratio:

This ratio is outlined by:

In our case, we acquire the next method:

(Observe that this makes use of weighted significance sampling, as an alternative of “naïve” significance sampling.)

We may after all compute these ratios naively in each step. Nevertheless, Sutton introduces a intelligent scheme updating these values (denoted by W) incrementally, which is far more environment friendly. In actual fact, in my authentic submit I confirmed the naive model, too — I consider this helps with understanding. Nevertheless, since right here we primarily care about benchmarking, and the “naïve” and the “incremental” model are similar, as much as efficiency — we right here solely listing the marginally extra advanced incremental model.

In pseudocode the corresponding algorithm seems to be as follows:

Observe that, against our preliminary submit introducing these strategies, the place the habits coverage was merely randomly, right here we choose a greater one — specifically an ε-greedy one w.r.t. to the present Q-table.

For extra particulars right here’s my corresponding submit on MC strategies.

Outcomes

With that, let’s evaluate these three algorithms on small Gridworld environments. Observe that one step right here denotes one full episode generated:

We observe off-policy MC to already trip at a Gridword dimension of 5×5, and, regardless that MC with ES and on-policy MC carry out higher, additionally they begin to wrestle with bigger sizes.

This could be considerably shocking, and disappointing for MC followers. Don’t fear, we’ll handle to spice up this — nevertheless it exhibits a weak point of those algorithms: in “giant” environments with sparse rewards, MC strategies principally need to hope to bump into the objective by likelihood — which decreases exponentially with the dimensions of the surroundings.

Thus, let’s try to make the duty simpler for the mannequin, and use the beforehand launched tips empirically discovered to assist efficiency of TD-learning: including intermediate rewards, and ε-decay — our “improved” setup.

In actual fact, with this all strategies fare a lot better:

Nevertheless, now MC ES is inflicting issues. Thus, let’s put this apart and proceed with out it: ES anyhow was a theoretical idea on the way in which of growing MC strategies, and clunky to make use of / implement (some would possibly bear in mind how I applied having the surroundings begin in random states …):

Right here, not less than we get near the outcomes of DP. Observe that I capped the maximal variety of steps to 100.000, so every time this quantity exhibits up within the graph it implies that the algorithm couldn’t clear up this surroundings within the given step restrict. On-policy MC really appears to carry out very well, the variety of steps wanted barely will increase— however off-policy MC appears to carry out worse.

Dialogue

To me, MC strategies carry out surprisingly properly — since they basically stumble across the surroundings randomly at first, hoping to seek out the objective by exploration alone. Nevertheless, after all this isn’t totally true — their efficiency (talking of on-policy MC) turns into actually good solely after enabling intermediate rewards — which information the mannequin in the direction of the objective. On this setup it appears MC strategies carry out very well — one potential cause being that they’re unbiased — and fewer delicate to hyperparameter tuning and co.

Temporal-Distinction Studying

Let’s come to TD strategies. These could be seen as combining the strengths of each approaches beforehand launched: much like MC, they don’t want a mannequin of the surroundings — however nonetheless they construct upon earlier estimates, they bootstrap — as in DP.

Let’s recap DP and MC fashions:

DP strategies flip the Bellman equation into an replace rule, and compute the worth of a state primarily based on the estimated values of its successor states:

MC strategies, then again, play out full episodes after which replace their worth estimates primarily based on the noticed return:

TD strategies mix these two concepts. They play out full episodes, however after each step replace worth estimates with the noticed return, and the earlier estimate:

Among the most basic RL algorithms stem from this area — and we’ll talk about them within the following.

Let’s start with Sarsa. First, we modify above launched replace rule to work with state-action pairs:

With this, Sarsa is definitely launched quite shortly: we play episodes, and replace values following our present coverage. The title comes from the tuples used within the updates:

In pseudocode this seems to be as follows:

Subsequent up we have now Q-learning. That is similar to Sarsa, with one key distinction: it’s an off-policy algorithm. As an alternative of merely following the executed transition through the replace, we take the utmost Q-value of all successor states:

You may image this as making a habits coverage b, which is the same as π, besides being grasping within the transitions underneath query.

The pseudocode seems to be like this:

One other algorithm is Anticipated Sarsa, which (you guessed it) — is an extension of Sarsa. As an alternative of following the one transition executed by the coverage, we account for all attainable successor states, and weigh them by how doubtless they’re given the present coverage:

The final algorithm on this chapter is an extension of Q-learning. Q-learning suffers from an issue often called maximization bias: because it makes use of a most over anticipated values, the ensuing estimate can have constructive bias. We are able to handle this through the use of two Q-tables: for every replace we use one for choosing a value-maximizing motion, and the opposite for computing the replace goal. Which is used the place is decided by a coin flip. The algorithm is named Double Q-learning:

Outcomes

Let’s take a look on the outcomes, beginning with the naïve surroundings:

We are able to see that each Q-learning strategies begin to get issues with Gridworld sizes of 11 x 11.

Thus let’s apply our recognized tips, yielding the “improved” setup:

All strategies can now discover options considerably faster — simply Anticipated Sarsa falls out. This might very properly be — it’s considerably much less used than Q-learning or Sarsa, and possibly extra a theoretical idea.

Thus, let’s proceed with out this technique and see how giant world sizes we will clear up:

Q-learning can now additionally clear up grid sizes of 25 x 25 with out issues — however Sarsa and Double Q-learning begin to degrade.

Extra particulars could be present in my introductory submit about TD strategies.

Dialogue

Within the improved setup, TD strategies typically carry out properly. We solely eradicated Anticipated Sarsa early, which anyhow is just not such a typical algorithm.

“Easy” Sarsa and Double Q-learning wrestle for bigger surroundings sizes, whereas Q-learning performs properly total. The latter is considerably shocking, since Double Q-learning ought to handle among the shortcomings of ordinary Q-learning, particularly the excessive variance. Doubtlessly, we already scale back the variance by working every experiment n instances. One other speculation could possibly be that Double Q-learning takes longer to converge, for the reason that variety of parameters has additionally doubled — which might point out that the facility of Double Q-learning exhibits higher for extra advanced issues with extra time.

As talked about performs Q-learning higher than Sarsa. This mirrors what can see in analysis / literature, specifically that Q-learning is considerably extra common. This may in all probability defined by it being off-policy, which often yields extra highly effective answer strategies. Sarsa then again performs higher for stochastic or “harmful” duties: since in Sarsa the precise chosen motion is taken under consideration within the worth replace, it higher understands the consequences of its actions, which is useful for stochastic environments and / or environments the place one can, e.g., fall off a cliff. Regardless of the latter being the case right here, the surroundings might be not advanced or giant sufficient, that this impact comes into play.

TD-n

TD-n strategies in a approach marry classical TD studying and MC strategies. As Sutton so properly places it, they “free us from the tyranny of the timestep” [1]. In MC strategies, we’re compelled to attend a full episode earlier than making any updates. In TD strategies, we replace estimates in each step — however are additionally compelled to solely look one step sooner or later.

Thus, it is smart to introduce n-step returns:

With that, we will merely introduce Sarsa-n:

We play episodes following the present coverage, after which replace the worth estimates with the n-step return.

In my corresponding submit, we additionally introduce an off-policy model of this. Nevertheless, to not blow up this submit too lengthy, and damaging expertise with off-policy MC strategies, we concentrate on the “classics” — comparable to Sarsa-n — and tree-n tree backup, which we introduce subsequent.

n-step tree backup is an extension of the beforehand seen Anticipated Sarsa. When computing the n-step return, the corresponding transition tree seems to be as follows:

I.e., there’s a single path down the tree similar to the precise motion taken. Simply as in Anticipated Sarsa, we now wish to weigh actions in keeping with their likelihood decided by the coverage. However since now we have now a tree of depth > 1, the cumulative worth of later ranges is weighted by the likelihood of the motion taken to achieve these ranges:

The pseudocode seems to be as follows:

Right here’s my corresponding submit on n-step TD strategies.

Outcomes

As common, we begin with the “naïve” setting, and acquire the next outcomes:

Sarsa-n begins to wrestle already with smaller grid world sizes. Let’s see if the improved setup adjustments this:

Now certainly Sarsa-n performs a lot better, however n-step tree backup doesn’t.

Dialogue

I discovered this discovery surprising and considerably laborious to elucidate. I’d love to listen to your ideas on this — however within the meantime I used to be chatting with my chat agent of alternative, and got here to this speculation: intermediate rewards probably confuse the tree algorithm, because it must study an identical return distribution over all attainable actions. Additional, the extra ε decays, the extra the anticipated distribution would possibly differ from the habits coverage.

Mannequin-Based mostly Reinforcement Studying / Planning

Within the earlier chapter we mentioned the subject “planning” — within the RL context with this we primarily seek advice from model-based strategies. That’s: we have now (or construct) a mannequin of the surroundings, and use this mannequin to discover additional “nearly”, and particularly use these explorations for extra and higher updates / learnings of the worth perform. The next picture shows the mixing of planning into studying very properly:

Within the top-right nook we see the “classical” RL coaching loop (additionally dubbed “direct” RL): beginning with some worth perform / coverage we act within the (actual) surroundings, and use this expertise to replace our price perform (or coverage within the case of policy-gradient strategies). When incorporating planning, we moreover additionally study a mannequin of the world from this expertise, after which use this mannequin to generate additional (digital) expertise, and replace our price or coverage perform from this.

This really is strictly the Dyna-Q algorithm, which seems to be as follows in pseudocode:

Steps (a) — (d) are our classical Q-learning, whereas the remainder of the algorithm provides the novel planning performance, particularly the world mannequin studying.

One other associated algorithm is Prioritized Sweeping, which adjustments how we pattern states for the “planning loop”: we discover and play in the true surroundings, whereas studying the mannequin, and save state-action pairs with giant anticipated worth adjustments to a queue. Solely with this queue we begin the “planning loop”, i.e. one thing to the steps (e) and (f) above:

Extra particulars could be present in my earlier submit on model-based RL strategies.

Outcomes

Let’s begin with the naïve setting:

Dyna Q performs moderately properly, whereas Prioritized Sweeping struggles early on.

Within the improved setting we see an identical factor:

Dialogue

Prioritized sweeping already carried out poorly within the corresponding introductory submit — I believe there both is a few subject, or extra doubtless this merely is a “tuning” factor — i.e. utilizing a fallacious sampling distribution.

Dyna-Q yields strong outcomes.

Benchmarking the Finest Algorithms

We’ve now seen the efficiency of all algorithms from Half I of Sutton’s guide by benchmarking them per chapter and on Gridworlds of as much as dimension 25 x 25. Already right here we noticed higher and worse performing algorithms, and particularly already discarded just a few candidates not suited to bigger environments.

Now we wish to benchmark the remaining ones — the perfect ones from every chapter — towards each other, on Gridworlds as much as dimension 50 x 50.

These algorithms are:

worth iteration
on-policy MC
Q-learning
Sarsa-n
Dyna-Q

Outcomes

Right here’s how they carry out on Gridworld, this time with a maximal step restrict of 200.000:

Let’s additionally plot the corresponding time wanted (observe that I plot unsuccessful runs — runs reaching the maximal variety of steps with out producing a possible coverage — at 500s):

We are able to observe a number of fascinating details from these figures:

The variety of steps vs. time wanted is very correlated.
Worth iteration performs exceptionally properly, fixing even Gridworlds of dimension 50 x 50 with ease, and doing so magnitudes quicker than the next-best algorithm.
The rating for the remaining algorithms is (higher to worse): On-policy MC, Dyna-Q, Q-learning, Sarsa-n.

Within the subsequent part we talk about these in additional particulars.

Dialogue

1. Steps vs. Time

We began this submit with a dialogue on which metrics / measurement to make use of, and — particularly — whether or not to make use of variety of steps or time wanted to unravel the issue. Wanting again, we will say that this dialogue was not so related in spite of everything, and — considerably surprisingly — these two numbers are extremely correlated. That’s, even supposing, as initially described, one “step” can differ relying on the algorithm.

2. Worth Iteration Dominates

Worth Iteration carried out remarkably properly, fixing even giant Gridworlds (as much as 50×50) with ease—outpacing all different algorithms by a large margin. This could be shocking, contemplating that DP strategies are sometimes thought-about theoretical instruments, hardly ever utilized in observe. Actual-world functions are inclined to favor strategies like Q-learning [2], PPO [4], or MCTS [5].

So why does such a “textbook” technique dominate right here? As a result of this surroundings is tailored for it:

The mannequin is totally recognized.
The dynamics are easy and deterministic.
The state area is comparatively small.

These are precisely the situations underneath which DP thrives. In distinction, model-free strategies like Q-learning are designed for settings the place such data is not out there. Their energy lies in generality and scalability, not in exploiting small, well-defined issues. Q-learning incurs excessive variance and requires many episodes to converge—disadvantages which are magnified in small-scale environments. In brief, there’s a transparent trade-off between effectivity and generality. We’ll revisit this level in a future submit after we introduce perform approximation, the place Q-learning has extra room to shine.

3. A Rating Emerges

Past Worth Iteration, we noticed the next efficiency rating: On-policy MC > Dyna-Q > Q-learning > Sarsa-n

On-policy Monte Carlo emerged because the best-performing model-free algorithm. This suits with our earlier reasoning: MC strategies are easy, unbiased, and well-suited to issues with deterministic objectives—particularly when episodes are comparatively brief. Whereas not scalable to giant or steady issues, MC strategies appear to be fairly efficient in small to medium-sized duties like Gridworld.

Dyna-Q comes subsequent. This end result reinforces our expectations: Dyna-Q blends model-based planning with model-free studying. Though the mannequin is realized (not given, as in Worth Iteration), it’s nonetheless easy and deterministic right here—making the realized mannequin helpful. This boosts efficiency considerably over pure model-free approaches.

Q-learning, whereas nonetheless highly effective, underperforms on this context for the explanations mentioned above: it’s a general-purpose algorithm that isn’t in a position to totally leverage the construction of straightforward environments.

Sarsa-n landed in final place. A probable rationalization is the added bias launched by bootstrapping in its multi-step updates. Not like Monte Carlo strategies, which estimate returns from full trajectories (unbiased), Sarsa-n makes use of bootstrapped estimates of future rewards. In small environments, this bias can outweigh the advantages of decreased variance.

Lastly, let’s evaluate our outcomes vs. those from Sutton:

Observe that Sutton lists the entire variety of steps on the x-axis, whereas we listing n, with the entire variety of states being n x n. For 376 states, Sutton report ~100k steps earlier than the optimum answer is discovered, whereas we report 75k for 400 states (20 x 20), contemplating Dyna-Q. The numbers are extremely comparable and supply a reassuring validation of our setup and implementation.

Conclusion

This submit served each as a recap of our collection on Half I of Sutton and Barto’s Reinforcement Studying [1]and as an extension past the guide’s scope—by benchmarking all launched algorithms on more and more bigger Gridworld environments.

We started by outlining our benchmarking setup, then revisited the core chapters of Half I: Dynamic Programming, Monte Carlo strategies, Temporal-Distinction studying, and Mannequin-Based mostly RL / Planning. In every part, we launched key algorithms comparable to Q-learning, offered full Python implementations, and evaluated their efficiency on Gridworlds as much as dimension 25×25. The objective of this preliminary spherical was to establish prime performers from every algorithmic household. Based mostly on our experiments, the standouts had been:
Worth Iteration, On-policy MC, Q-learning, Sarsa-n, and Dyna-Q. Python code to breed these outcomes, and particularly implementations of all mentioned strategies, is out there on GitHub.

Subsequent, we stress-tested these high-performers on bigger environments (as much as 50×50) and noticed the next rating:
Worth Iteration > On-policy MC > Dyna-Q > Q-learning > Sarsa-n

Whereas this end result could also be shocking—given the widespread use of Q-learning and the comparatively uncommon software of Worth Iteration and MC strategies—it is smart in context. Easy, fully-known, deterministic environments are perfect for Worth Iteration and MC strategies. In distinction, Q-learning is designed for extra advanced, unknown, and high-variance environments the place perform approximation turns into obligatory. As we mentioned, there’s a trade-off between effectivity in structured duties and generality in advanced ones.

That brings us to what’s subsequent. In upcoming posts, we’ll push the boundaries additional:

First, by benchmarking these strategies in tougher environments comparable to two-player video games, the place direct competitors will expose their variations extra starkly.
Then, we’ll dive into Half II of Sutton’s guide, the place perform approximation is launched. This unlocks the power to scale reinforcement studying to environments far past what tabular strategies can deal with.

In the event you’ve made it this far—thanks for studying! I hope you loved this deep dive, and I’d like to have you ever again for the subsequent installment within the collection.