- The paper introduces novel on-policy bisimulation metrics that efficiently compute state similarity in deterministic MDPs.
- It presents two algorithms—one using sampling with guaranteed convergence and another with differentiable neural approximations—to scale computations in large state spaces.
- Empirical results on GridWorld and Atari 2600 demonstrate enhanced state aggregation, abstraction, and policy transfer in reinforcement learning.
Scalable Methods for Computing State Similarity in Deterministic Markov Decision Processes
The paper addresses a challenge in the computation and approximation of bisimulation metrics for Markov Decision Processes (MDPs), specifically tailored towards deterministic scenarios. Historically, bisimulation metrics have been recognized for their theoretical appeal in representing state similarity, which in turn aids in planning and reinforcement learning tasks. These metrics essentially encode behavioral equivalence between MDP states, providing guarantees about the variability in optimal policies. Yet, practical application has been hindered by computational costs due primarily to the need for a full tabular state representation.
One of the paper's significant departures is the introduction of a new variant of bisimulation metrics. This variant operates according to a specified behavior policy, termed "on-policy" bisimulation. This contrasts with traditional approaches which assess equivalence based on all possible actions, a requirement that can lead to overly pessimistic and complex evaluations. The on-policy variant aligns more closely with practical scenarios, targeting relevant behaviors rather than worst-case actions that may rarely be chosen by any sensible policy.
Two algorithms are proposed to make these computations feasible in environments characterized by large or continuous state spaces. The first algorithm employs a sampling technique that promises convergence to the true bisimulation metric, thus sidestepping the need for exhaustive state exploration. The second method introduces a differentiable loss function enabling neural networks to approximate bisimulation metrics even amidst continuous state spaces—a previously unattainable feature.
The paper provides empirical validation of these methods on a discrete, small-scale GridWorld and proceeds to demonstrate applicability on larger-scale problems involving the Atari 2600 suite. Notably, in these larger settings, representations from deep reinforcement learning agents are utilized, adjusting the policy-based bisimulation approximant to evaluate similarities relative to learned policies by such agents.
Crucially, the paper discusses the implications of these developments. The learning of approximants for bisimulation metrics holds promise for facilitating tasks like state aggregation, abstraction, and policy transfer in environments where traditional tabular evaluations are computationally prohibitive. By using neural networks, the authors suggest a pathway to latent space representations that not only respect the theoretical properties of bisimulation metrics but also offer practical utility in complex environments.
The paper indicates several future directions, one being the extension of these techniques to stochastic systems which introduce additional complexity into the transition dynamics of MDPs. Another promising avenue is leveraging bisimulation metrics as auxiliary objectives within learning frameworks, potentially enhancing overall agent performance by encapsulating important state similarities beyond immediate rewards.
In summary, this work presents innovative methods to compute and approximate bisimulation metrics on a scalable level, potentially influencing both theoretical explorations and practical implementations in reinforcement learning and related fields. This could lead to enhanced decision-making capacities and more robust policy derivations in AI systems facing large or complex decision spaces.