Conference Paper

# Policy Gradient Semi-Markov Decision Process

DOI: 10.1109/ICTAI.2008.51 Conference: 20th IEEE International Conference on Tools with Artificial Intelligence (ICTAI 2008), November 3-5, 2008, Dayton, Ohio, USA, Volume 2

Source: DBLP

**ABSTRACT**

This paper proposes a simulation-based algorithm for optimizing the average reward in a parameterized continuous-time, finite-state semi-Markov decision process (SMDP). Our contributions are twofold: First, we compute the approximate gradient of the average reward with respect to the parameters in SMDP controlled by parameterized stochastic policies. Then stochastic gradient ascent method is used to adjust the parameters in order to optimize the average reward. Second, we present a simulation-based algorithm to estimate the approximate average gradient of the average reward (GSMDP), using only single sample path of the underlying Markov chain. We prove the almost sure convergence of this estimate to the true gradient of the average reward when the number of iterations goes to infinity.

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**ABSTRACT:**In [1] and [2] we have presented a simulation-based algorithm for optimizing the average reward in a parameterized continuous-time, finite-state semi-Markov Decision Process (SMDP). We approximated the gradient of the average reward. Then, a simulation-based algorithm was proposed to estimate the approximate gradient of the average reward (called GSMDP), using only a single sample path of the underlying Markov chain. GSMDP was proved to converge with probability 1. In this paper, we give bounds on the approximation and estimation errors for GSMDP algorithm. The approximation error of that approximation is the size of the difference between the true gradient and the approximate gradient. The estimation error, the size of the difference between the output of the algorithm and its asymptotic output, arises because the algorithm sees only a finite data sequence.IEICE Transactions on Information and Systems 02/2010; 93-D(2):271-279. DOI:10.1587/transinf.E93.D.271 · 0.21 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**In this paper, we propose to use hierarchical action decomposition to make Bayesian model-based reinforcement learning more efficient and feasible for larger problems. We formulate Bayesian hierarchical reinforcement learning as a partially observable semi-Markov decision process (POSMDP). The main POSMDP task is partitioned into a hierarchy of POSMDP subtasks. Each subtask might consist of only primitive actions or hierarchically call other subtasks’ policies, since the policies of lower-level subtasks are considered as macro actions in higher-level subtasks. A solution for this hierarchical action decomposition is to solve lower-level subtasks first, then higher-level ones. Because each formulated POSMDP has a continuous state space, we sample from a prior belief to build an approximate model for them, then solve by using a recently introduced Monte Carlo Value Iteration with Macro-Actions solver. We name this method Monte Carlo Bayesian Hierarchical Reinforcement Learning. Simulation results show that our algorithm exploiting the action hierarchy performs significantly better than that of flat Bayesian reinforcement learning in terms of both reward, and especially solving time, in at least one order of magnitude.Applied Intelligence 10/2014; 41(3). DOI:10.1007/s10489-014-0565-6 · 1.85 Impact Factor

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