Epistemic POMDPs and Implicit Partial Observability – The Berkeley Synthetic Intelligence Analysis Weblog

Many experimental works have noticed that generalization in deep RL seems to be troublesome: though RL brokers can study to carry out very complicated duties, they don’t appear to generalize over numerous job distributions in addition to the superb generalization of supervised deep nets would possibly lead us to anticipate. On this weblog submit, we are going to goal to elucidate why generalization in RL is basically tougher, and certainly harder even in principle.

We’ll present that trying to generalize in RL induces implicit partial observability, even when the RL drawback we are attempting to resolve is a normal fully-observed MDP. This induced partial observability can considerably complicate the forms of insurance policies wanted to generalize effectively, doubtlessly requiring counterintuitive methods like information-gathering actions, recurrent non-Markovian conduct, or randomized methods. Ordinarily, this isn’t crucial in absolutely noticed MDPs however surprisingly turns into crucial once we take into account generalization from a finite coaching set in a completely noticed MDP. This weblog submit will stroll by way of why partial observability can implicitly come up, what it means for the generalization efficiency of RL algorithms, and the way strategies can account for partial observability to generalize effectively.

Studying By Instance

Earlier than formally analyzing generalization in RL, let’s start by strolling by way of two examples that illustrate what could make generalizing effectively in RL issues troublesome.

The Picture Guessing Recreation: On this recreation, an RL agent is proven a picture every episode, and should guess its label as shortly as potential (Determine 1). Every timestep, the agent makes a guess; if the agent is appropriate, then the episode ends, but when incorrect, the agent receives a detrimental reward, and should make one other guess for a similar picture on the subsequent timestep. Since every picture has a singular label (that’s, there’s some “true” labelling operate $f_{true}: x mapsto y$) and the agent receives the picture as statement, it is a fully-observable RL setting.

Fig 1. The picture guessing recreation, which requires an agent to repeatedly guess labels for a picture till it will get it appropriate. RL learns insurance policies that guess the identical label repeatedly, a method that generalizes poorly to check photos (backside row, proper).

Suppose we had entry to an infinite variety of coaching photos, and discovered a coverage utilizing a normal RL algorithm. This coverage will study to deterministically predict the true label ($y := f_{true}(x)$), since that is the best return technique within the MDP (as a sanity verify, recall that the optimum coverage in an MDP is deterministic and memoryless). If we solely have a restricted set of coaching photos, an RL algorithm will nonetheless study the identical technique, deterministically predicting the label it believes matches the picture. However, does this coverage generalize effectively? On an unseen check picture, if the agent’s predicted label is appropriate, the best potential reward is attained; if incorrect, the agent receives catastrophically low return, because it by no means guesses the proper label. This catastrophic failure mode is ever-present, since despite the fact that fashionable deep nets enhance generalization and scale back the prospect of misclassification, error on the check set can’t be utterly diminished to 0.

Can we do higher than this deterministic prediction technique? Sure, for the reason that discovered RL technique ignores two salient options of the guessing recreation: 1) the agent receives suggestions by way of an episode as as to if its guesses are appropriate, and a pair of) the agent can change its guess in future timesteps. One technique that higher takes benefit of those options is process-of-elimination; first, choosing the label it considers almost certainly, and if incorrect, eliminating it and adapting to the following most-likely label, and so forth. One of these adaptive memory-based technique, nevertheless, can by no means be discovered by a normal RL algorithm like Q-learning, since they optimize MDP aims and solely study deterministic and memoryless insurance policies.

Maze-Fixing: A staple of RL generalization benchmarks, the maze-solving drawback requires an agent to navigate to a aim in a maze given a birds-eye view of the entire maze. This job is fully-observed, for the reason that agent’s statement exhibits the entire maze. Because of this, the optimum coverage is memoryless and deterministic: taking the motion that strikes the agent alongside the shortest path to the aim. Simply as within the image-guessing recreation, by maximizing return inside the coaching maze layouts, an RL algorithm will study insurance policies akin to this “optimum” technique – at any state, deterministically taking the motion that it considers almost certainly to be on the shortest path to the aim.

This RL coverage generalizes poorly, since if the discovered coverage ever chooses an incorrect motion, like working right into a wall or doubling again on its previous path, it can proceed to loop the identical mistake and by no means resolve the maze. This failure mode is totally avoidable, since even when the RL agent initially takes such an “incorrect” motion, after trying to comply with it, the agent receives info (e.g. the following statement) as as to if or not this was a very good motion. To generalize in addition to potential, an agent ought to adapt its chosen actions if the unique actions led to surprising outcomes , however this conduct eludes customary RL aims.

Fig 2. Within the maze job, RL insurance policies generalize poorly: after they make an error, they repeatedly make the identical error, resulting in failure (left). An agent that generalizes effectively should make errors, however has the potential of adapting and recovering from these errors (proper). This conduct shouldn’t be discovered by customary RL aims for generalization.

What’s Going On? RL and Epistemic Uncertainty

In each the guessing recreation and the maze job, the hole between conduct discovered by customary RL algorithms and by insurance policies that truly generalize effectively, appeared to come up when the agent incorrectly (or couldn’t) recognized how the dynamics of the world behave. Let’s dig deeper into this phenomenon.

Fig 3. The restricted coaching dataset prevents an agent from precisely recovering the true setting. As a substitute, there’s an implicit partial observability, as an agent doesn’t know which amongst the set of “constant” environments is the true setting.

When the agent is given a small coaching set of contexts, there are various dynamics fashions that match the offered coaching contexts, however differ on held-out contexts. These conflicting hypotheses epitomize the agent’s epistemic uncertainty from the restricted coaching set. Whereas uncertainty shouldn’t be particular to RL, how it may be dealt with in RL is exclusive as a result of sequential determination making loop. For instance, the agent can actively regulate how a lot epistemic uncertainty it’s uncovered to, for instance by selecting a coverage that solely visits states the place the agent is very assured in regards to the dynamics. Much more importantly, the agent can change its epistemic uncertainty at analysis time by accounting for the knowledge that it receives by way of the trajectory. Suppose for a picture within the guessing recreation, the agent is initially unsure between the t-shirt / coat labels. If the agent guesses “t-shirt” and receives suggestions that this was incorrect, the agent adjustments its uncertainty and turns into extra assured in regards to the “coat” label, that means it ought to consequently adapt and guess “coat” as a substitute.

Epistemic POMDPs and Implicit Partial Observability

Actively steering in direction of areas of low uncertainty or taking information-gathering actions are two of a large number of avenues an RL agent has to deal with its epistemic uncertainty. Two vital questions stay unanswered: is there a “finest” approach to sort out uncertainty? If that’s the case, how can we describe it? From the Bayesian perspective, it seems there’s an optimum resolution: generalizing optimally requires us to resolve {a partially} noticed MDP (POMDP) that’s implicitly created from the agent’s epistemic uncertainty.

This POMDP, which we name the epistemic POMDP, works as follows. Recall that as a result of the agent has solely seen a restricted coaching set, there are various potential environments which might be according to the coaching contexts offered. The set of constant environments will be encoded by a Bayesian posterior over environments $P(M mid D)$. Every episode within the epistemic POMDP, an agent is dropped into one among these “constant” environments $M sim P(M mid D)$, and requested to maximise return inside it, however with the next vital element: the agent shouldn’t be informed which setting $M$ it was positioned in.

This technique corresponds to a POMDP (partially noticed MDP), for the reason that related info wanted to behave is barely partially observable to the agent: though the state $s$ inside the setting is noticed, the identification of the setting $M$ that’s producing these states is hidden from the agent. The epistemic POMDP supplies an instantiation of the generalization drawback into the Bayesian RL framework (see survey right here), which extra typically research optimum conduct underneath distributions over MDPs.

Fig 4. Within the epistemic POMDP, an agent interacts with a special “constant” setting in every episode, however doesn’t know which one it’s interacting with, resulting in partial observability. To do effectively, an agent should make use of a (doubtlessly memory-based) technique that works effectively irrespective of which of those environments it’s positioned in.

Let’s stroll by way of an instance of what the epistemic POMDP appears like. For the guessing recreation, the agent is unsure about precisely how photos are labelled, so every potential setting $M sim P(M mid D)$ corresponds to a special picture labeller that’s according to the coaching dataset: $f_M: X to Y$. Within the epistemic POMDP for the guessing recreation, every episode, a picture $x$ and labeller $f_M$ are chosen at random, and the agent required to output the label that’s assigned by the sampled classifier $y = f_M(x)$. The agent can’t do that immediately, as a result of the identification of the classifier $f_M$ is not offered to the agent, solely the picture $x$. If all of the labellers $f_M$ within the posterior agree on the label for a sure picture, the agent can simply output this label (no partial observability). Nonetheless, if completely different classifiers assign completely different labels, the agent should use a method that works effectively on common, no matter which of the labellers was used to label the info (for instance, by adaptive process-of-elimination guessing or randomized guessing).

What makes the epistemic POMDP significantly thrilling is the next equivalence:

An RL agent is Bayes-optimal for generalization if and provided that it maximizes anticipated return within the corresponding epistemic POMDP. Extra typically, the efficiency of an agent within the epistemic POMDP dictates how effectively it’s anticipated to generalize at analysis time.

That generalization efficiency is dictated by efficiency within the epistemic POMDP hints at a couple of classes for bridging the hole between the “optimum” approach to generalize in RL and present practices. For instance, it’s comparatively well-known that the optimum coverage in a POMDP is mostly non-Markovian (adaptive based mostly on historical past), and should take information-gathering actions to scale back the diploma of partial observability. Which means that to generalize optimally, we’re prone to want adaptive information-gathering behaviors as a substitute of the static Markovian insurance policies which might be often educated.

The epistemic POMDP additionally highlights the perils of our predominant method to studying insurance policies from a restricted coaching set of contexts: working a fully-observable RL algorithm on the coaching set. These algorithms mannequin the setting as an MDP and study MDP-optimal methods, that are deterministic and Markov. These insurance policies don’t account for partial observability, and due to this fact are inclined to generalize poorly (for instance, within the guessing recreation and maze duties). This means a mismatch between the MDP-based coaching aims which might be customary in fashionable algorithms and the epistemic POMDP coaching goal that truly dictates how effectively the discovered coverage generalizes.

Shifting Ahead with Generalization in RL

The implicit presence of partial observability at check time could clarify why customary RL algorithms, which optimize fully-observed MDP aims, fail to generalize. What ought to we do as a substitute to study RL insurance policies that generalize higher? The epistemic POMDP supplies a prescriptive resolution: when the agent’s posterior distribution over environments will be calculated, then developing the epistemic POMDP and working a POMDP-solving algorithm on it can yield insurance policies that generalize Bayes-optimally.

Sadly, in most fascinating issues, this can’t be precisely carried out. Nonetheless, the epistemic POMDP can function a lodestar for designing RL algorithms that generalize higher. As a primary step, in our NeurIPS 2021 paper, we introduce an algorithm referred to as LEEP, which makes use of statistical bootstrapping to study a coverage in an approximation of the epistemic POMDP. On Procgen, a difficult generalization benchmark for RL brokers, LEEP improves considerably in test-time efficiency over PPO (Determine 3). Whereas solely a crude approximation, LEEP supplies some indication that trying to study a coverage within the epistemic POMDP is usually a fruitful avenue for growing extra generalizable RL algorithms.

Fig 5. LEEP, an algorithm based mostly on the epistemic POMDP goal, generalizes higher than PPO in 4 Procgen duties.

---

In case you take one lesson from this weblog submit…

In supervised studying, optimizing for efficiency on the coaching set interprets to good generalization efficiency, and it’s tempting to suppose that generalization in RL will be solved in the identical method. That is surprisingly not true; restricted coaching information in RL introduces implicit partial observability into an in any other case fully-observable drawback. This implicit partial observability, as formalized by the epistemic POMDP, implies that generalizing effectively in RL necessitates adaptive or stochastic behaviors, hallmarks of POMDP issues.

In the end, this highlights the incompatibility that afflicts generalization of our deep RL algorithms: with restricted coaching information, our MDP-based RL aims are misaligned with the implicit POMDP goal that finally dictates generalization efficiency.

This submit is predicated on the paper “Why Generalization in RL is Tough: Epistemic POMDPs and Implicit Partial Observability,” which is joint work with Jad Rahme (equal contribution), Aviral Kumar, Amy Zhang, Ryan P. Adams, and Sergey Levine. Because of Sergey Levine and Katie Kang for useful suggestions on the weblog submit.