PEGASUS: A Policy Search Method for Large MDPs and POMDPs

Abstract: We propose a new approach to the problem of searching a space of policies for a Markov decision process (MDP) or a partially observable Markov decision process (POMDP), given a model. Our approach is based on the following observation: Any (PO)MDP can be transformed into an "equivalent" POMDP in which all state transitions (given the current state and action) are deterministic. This reduces the general problem of policy search to one in which we need only consider POMDPs with deterministic transitions. We give a natural way of estimating the value of all policies in these transformed POMDPs. Policy search is then simply performed by searching for a policy with high estimated value. We also establish conditions under which our value estimates will be good, recovering theoretical results similar to those of Kearns, Mansour and Ng (1999), but with "sample complexity" bounds that have only a polynomial rather than exponential dependence on the horizon time. Our method applies to arbitrary POMDPs, including ones with infinite state and action spaces. We also present empirical results for our approach on a small discrete problem, and on a complex continuous state/continuous action problem involving learning to ride a bicycle.

• The paper introduces a deterministic simulative model that transforms MDPs and POMDPs into equivalent deterministic systems, streamlining policy evaluation.
• It demonstrates that PEGASUS achieves polynomial sample complexity, making policy optimization tractable in large-scale environments.
• Empirical evaluations show that PEGASUS efficiently converges in continuous domains, offering promising applications in robotics and autonomous systems.

Analyzing PEGASUS: A Policy Search Method for Large MDPs and POMDPs

The paper authored by Andrew Y. Ng and Michael Jordan presents PEGASUS, an innovative policy search method tailored for large-scale Markov decision processes (MDPs) and partially observable MDPs (POMDPs). The core contribution lies in transforming these complex environments into simpler, deterministic equivalents, facilitating effective policy evaluation and search.

Methodology and Theoretical Contributions

PEGASUS introduces a novel transformation of (PO)MDPs, asserting that any such process can be reconstituted into an "equivalent" POMDP characterized by deterministic state transitions. This transformation hinges on a deterministic simulative model that, unlike traditional generative models, draws on predefined randomness, eliminating internal stochastic elements.

Key steps in the PEGASUS approach include:

1. Deterministic Simulative Model: By assuming access to a deterministic model, the paper bypasses traditional stochasticity, instead utilizing external random number provision to simulate transitions.
2. Policy Evaluation: The method evaluates policies by approximating value functions through deterministic sampling, significantly reducing the high dimensional reliance on stochastic calculations.
3. Polynomial Sample Complexity: The analysis demonstrates that PEGASUS achieves polynomial dependence on horizon time, contrasting sharply with traditional methods which often suffer from exponential growth in complexity. This improvement is critical for practical applicability in large state and action spaces.

Empirical and Theoretical Results

The authors substantiate their theoretical contributions with empirical evaluations, showing notable performance improvements in both discrete and continuous domains. The experiments demonstrate the capability of PEGASUS to efficiently converge to viable policies even with complex continuous action tasks, such as learning to ride a bicycle.

Theoretical insights include uniform convergence results contingent on the complexity of the policy class and the transformations applied. The paper advances the understanding of how policy complexities and deterministic simulations interact, providing a comprehensive framework for ensuring uniform convergence across various dimensions.

Implications and Future Directions

From a theoretical standpoint, these results offer deeper insight into policy evaluation mechanisms within deterministic simulations, suggesting a pathway for extending these techniques to infinite state spaces and action sets.

Practically, the ability to model POMDPs as deterministic systems paves the way for deploying PEGASUS in real-world scenarios, ranging from robotics to autonomous decision-making systems, where efficient policy optimization in complex environments is crucial.

Future work might explore further reducing the reliance on extensive scenario sampling, enhancing the method's scalability. Investigating alternative deterministic transformations or extending the approach to collaborative multi-agent systems could also provide significant advancements.

In conclusion, the PEGASUS framework marks a significant step in policy search methodologies, offering a robust strategy for addressing the inherent complexities of large MDPs and POMDPs. The formal approach, rooted in deterministic modeling, establishes a foundation upon which future research may build, further bridging the gap between theoretical insights and practical applications in AI.