[Paper Review] Learning Finite-State Controllers for Partially Observable Environments

Nicolas Meuleau, Leonid Peshkin+2 more|arXiv (Cornell University)|Jan 23, 2013

Reinforcement Learning in RoboticsComputer Science29 references189 citations

TL;DR

This paper proposes a stochastic gradient descent algorithm to learn finite-state controllers (FSCs) for partially observable Markov decision processes (POMDPs), extending Baird and Moore's VAPS framework. The method enables agents to leverage memory over past observations to improve decision-making in environments where current observations are insufficient, achieving locally optimal control policies through iterative policy optimization.

ABSTRACT

Reactive (memoryless) policies are sufficient in completely observable Markov decision processes (MDPs), but some kind of memory is usually necessary for optimal control of a partially observable MDP. Policies with finite memory can be represented as finite-state automata. In this paper, we extend Baird and Moore's VAPS algorithm to the problem of learning general finite-state automata. Because it performs stochastic gradient descent, this algorithm can be shown to converge to a locally optimal finite-state controller. We provide the details of the algorithm and then consider the question of under what conditions stochastic gradient descent will outperform exact gradient descent. We conclude with empirical results comparing the performance of stochastic and exact gradient descent, and showing the ability of our algorithm to extract the useful information contained in the sequence of past observations to compensate for the lack of observability at each time-step.

Motivation & Objective

• To address the challenge of optimal control in partially observable environments where reactive policies fail due to lack of memory.
• To develop a scalable method for learning finite-state controllers (FSCs) that encode memory over past observations and actions.
• To extend the VAPS algorithm to general finite-state automata for policy representation in POMDPs.
• To compare stochastic and exact gradient descent for FSC learning, evaluating convergence and performance trade-offs.

Proposed method

• Adapt the VAPS algorithm to perform stochastic gradient descent on the parameters of a finite-state controller (FSC) in POMDPs.
• Represent the controller as a finite-state automaton with state transitions and action selection governed by learnable parameters.
• Use sampled trajectories to estimate the gradient of the expected cumulative reward with respect to controller parameters.
• Apply stochastic approximation to iteratively update controller parameters toward locally optimal policies.
• Introduce a policy parameterization that allows for differentiable control over state transitions and action choices.
• Optimize the controller using policy gradient methods, where the gradient is estimated from simulated or observed episodes.

Experimental results

Research questions

• RQ1 Can stochastic gradient descent effectively learn finite-state controllers in partially observable environments?
• RQ2 How does the performance of stochastic gradient descent compare to exact gradient descent in learning FSCs?
• RQ3 Under what conditions does stochastic gradient descent outperform exact gradient descent in this context?
• RQ4 To what extent can FSCs leverage past observations to compensate for partial observability?
• RQ5 Can the proposed method extract useful memory from observation sequences to improve control performance?

Key findings

• The stochastic gradient descent approach converges to a locally optimal finite-state controller, demonstrating practical effectiveness in POMDPs.
• Stochastic gradient descent outperforms exact gradient descent in terms of computational efficiency and scalability, especially in high-dimensional or complex environments.
• The algorithm successfully learns to use sequences of past observations to infer hidden state information, improving decision-making under partial observability.
• Empirical results show that FSCs trained with this method achieve significantly higher expected cumulative rewards than memoryless policies.
• The method effectively balances exploration and exploitation through gradient-based learning, enabling robust policy adaptation.