Experiments with Infinite-Horizon, Policy-Gradient Estimation (1106.0666v2)

Abstract: In this paper, we present algorithms that perform gradient ascent of the average reward in a partially observable Markov decision process (POMDP). These algorithms are based on GPOMDP, an algorithm introduced in a companion paper (Baxter and Bartlett, this volume), which computes biased estimates of the performance gradient in POMDPs. The algorithm's chief advantages are that it uses only one free parameter beta, which has a natural interpretation in terms of bias-variance trade-off, it requires no knowledge of the underlying state, and it can be applied to infinite state, control and observation spaces. We show how the gradient estimates produced by GPOMDP can be used to perform gradient ascent, both with a traditional stochastic-gradient algorithm, and with an algorithm based on conjugate-gradients that utilizes gradient information to bracket maxima in line searches. Experimental results are presented illustrating both the theoretical results of (Baxter and Bartlett, this volume) on a toy problem, and practical aspects of the algorithms on a number of more realistic problems.

Infinite-Horizon Policy-Gradient Estimation for POMDPs

The paper under consideration presents a comprehensive investigation into the domain of policy-gradient methods, specifically targeting infinite-horizon applications associated with partially observable Markov decision processes (POMDPs). The paper undertaken by Baxter et al. introduces novel algorithms that perform gradient ascent on the average reward of POMDPs. These algorithms leverage the GSEARCH method, which facilitates the computation of biased performance gradient estimates without necessitating knowledge about the underlying state—a notable advantage in complex environments with infinite state, control, and observation spaces.

Methodology and Algorithmic Framework

The core of the paper revolves around the GSEARCH approach for policy-gradient estimation. This method requires only a single free parameter, $\beta \in [0, 1)$, which serves as a bias-variance trade-off mechanism. Notably, GSEARCH can efficiently generate gradient estimates which can then be utilized in two divergent algorithmic strategies: a traditional stochastic gradient ascent, and a more sophisticated conjugate-gradient method. Both methods aim to optimize policies by leveraging gradient information through iterative improvements.

In the stochastic-gradient algorithm, parameter updates are executed at each iteration, ensuring a continuous adjustment that converges towards a local optimum of average rewards. In contrast, the conjugate-gradient algorithm benefits from a sophisticated novel line-search method for locating local maxima—a critical enhancement that circumvents issues associated with noisy value estimates.

Experimental Evaluation

Empirical results span across various scenarios including a simplified three-state MDP, the Puck World navigation task, the call-admission control problem, and a mountainous variant of the traditional mountain-car task. These experiments elucidate the potential of the proposed methods to reliably discover policies that are either near-optimal or markedly improve upon baselines. Particularly, results from the call-admission scenario highlight a substantial speed-up in convergence (1-2 orders of magnitude) compared to existing stochastic-gradient approaches.

One of the fascinating insights of the paper is the visualization of the bias-variance trade-off inherent in the choice of the parameter $\beta$, with lower values reducing variance but increasing bias, and vice versa. This trade-off is illustrated further through different configurations across experimental scenarios, underscoring the flexibility of the proposed approach.

Implications and Future Directions

The research outlined provides pivotal implications for both theoretical and practical applications. It extends the toolkit available for addressing POMDPs by introducing a scalable method that manages infinite-state spaces without relying on complete state information. Practitioners engaged in complex reinforcement learning tasks can employ these findings to enhance policy performance, particularly in domains where state space is vast and partially observable.

Theoretically, the work lays the groundwork for further exploration into actor-critic algorithms, which may amalgamate the rapid convergence characteristic of value-function methods with the robustness of policy-gradient approaches. These hybrid approaches could provide a balanced path towards highly efficient and scalable reinforcement learning deployments.

The scope for future research is vast. Potential avenues include the adaptation of these gradient-based approaches to distributed multi-agent systems, where independent agents can leverage gradient information to optimize collective objectives without centralized control. Also, advancing the understanding of automatic tuning of the bias-variance parameter $\beta$ could facilitate more hands-off deployment strategies, reducing the need for extensive parameter experimentation in practice.

Conclusion

In essence, Baxter et al.'s work on infinite-horizon policy-gradient estimation marks a significant contribution to the reinforcement learning field. By presenting robust methodologies validated across diverse applications, the paper pioneers avenues for deploying effective learning algorithms in environments characterized by partial observability and infinite state spaces. As AI continues its progression into complex, real-world tasks, contributions such as this will be instrumental in shaping efficient learning paradigms.