Policy Gradient Algorithms for Robust MDPs with Non-Rectangular Uncertainty Sets

• URL: http://arxiv.org/abs/2305.19004v3
• Date: Tue, 23 Jan 2024 09:59:27 GMT
• Title: Policy Gradient Algorithms for Robust MDPs with Non-Rectangular Uncertainty Sets
• Authors: Mengmeng Li, Daniel Kuhn, Tobias Sutter
• Abstract summary: We propose policy gradient algorithms for robust infinite-horizon Markov decision processes (MDPs) with non-rectangular uncertainty sets. The corresponding robust MDPs cannot be solved with dynamic programming techniques and are in fact provably intractable. We thus present the first complete solution scheme for robust MDPs with non-rectangular uncertainty sets offering global optimality guarantees.
• Score: 10.26382228865201
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose policy gradient algorithms for robust infinite-horizon Markov decision processes (MDPs) with non-rectangular uncertainty sets, thereby addressing an open challenge in the robust MDP literature. Indeed, uncertainty sets that display statistical optimality properties and make optimal use of limited data often fail to be rectangular. Unfortunately, the corresponding robust MDPs cannot be solved with dynamic programming techniques and are in fact provably intractable. We first present a randomized projected Langevin dynamics algorithm that solves the robust policy evaluation problem to global optimality but is inefficient. We also propose a deterministic policy gradient method that is efficient but solves the robust policy evaluation problem only approximately, and we prove that the approximation error scales with a new measure of non-rectangularity of the uncertainty set. Finally, we describe an actor-critic algorithm that finds an $\epsilon$-optimal solution for the robust policy improvement problem in $\mathcal{O}(1/\epsilon^4)$ iterations. We thus present the first complete solution scheme for robust MDPs with non-rectangular uncertainty sets offering global optimality guarantees. Numerical experiments show that our algorithms compare favorably against state-of-the-art methods.

Related papers

• Deterministic Trajectory Optimization through Probabilistic Optimal Control [3.2771631221674333]
  We propose two new algorithms for discrete-time deterministic finite-horizon nonlinear optimal control problems. Both algorithms are inspired by a novel theoretical paradigm known as probabilistic optimal control. We show that the application of this algorithm results in a fixed point of probabilistic policies that converge to the deterministic optimal policy.
  arXiv  Detail & Related papers  (2024-07-18T09:17:47Z)
• Global Algorithms for Mean-Variance Optimization in Markov Decision Processes [8.601670707452083]
  Dynamic optimization of mean and variance in Markov decision processes (MDPs) is a long-standing challenge caused by the failure of dynamic programming. We propose a new approach to find the globally optimal policy for combined metrics of steady-state mean and variance in an infinite-horizon undiscounted MDP.
  arXiv  Detail & Related papers  (2023-02-27T12:17:43Z)
• Policy Gradient for Rectangular Robust Markov Decision Processes [62.397882389472564]
  We introduce robust policy gradient (RPG), a policy-based method that efficiently solves rectangular robust Markov decision processes (MDPs) Our resulting RPG can be estimated from data with the same time complexity as its non-robust equivalent.
  arXiv  Detail & Related papers  (2023-01-31T12:40:50Z)
• Maximum-Likelihood Inverse Reinforcement Learning with Finite-Time Guarantees [56.848265937921354]
  Inverse reinforcement learning (IRL) aims to recover the reward function and the associated optimal policy. Many algorithms for IRL have an inherently nested structure. We develop a novel single-loop algorithm for IRL that does not compromise reward estimation accuracy.
  arXiv  Detail & Related papers  (2022-10-04T17:13:45Z)
• First-order Policy Optimization for Robust Markov Decision Process [40.2022466644885]
  We consider the problem of solving robust Markov decision process (MDP) MDP involves a set of discounted, finite state, finite action space MDPs with uncertain transition kernels. For $(mathbfs,mathbfa)$-rectangular uncertainty sets, we establish several structural observations on the robust objective.
  arXiv  Detail & Related papers  (2022-09-21T18:10:28Z)
• Softmax Policy Gradient Methods Can Take Exponential Time to Converge [60.98700344526674]
  The softmax policy gradient (PG) method is arguably one of the de facto implementations of policy optimization in modern reinforcement learning. We demonstrate that softmax PG methods can take exponential time -- in terms of $mathcalS|$ and $frac11-gamma$ -- to converge.
  arXiv  Detail & Related papers  (2021-02-22T18:56:26Z)
• Average-Reward Off-Policy Policy Evaluation with Function Approximation [66.67075551933438]
  We consider off-policy policy evaluation with function approximation in average-reward MDPs. bootstrapping is necessary and, along with off-policy learning and FA, results in the deadly triad. We propose two novel algorithms, reproducing the celebrated success of Gradient TD algorithms in the average-reward setting.
  arXiv  Detail & Related papers  (2021-01-08T00:43:04Z)
• Adaptive Sampling for Best Policy Identification in Markov Decision Processes [79.4957965474334]
  We investigate the problem of best-policy identification in discounted Markov Decision (MDPs) when the learner has access to a generative model. The advantages of state-of-the-art algorithms are discussed and illustrated.
  arXiv  Detail & Related papers  (2020-09-28T15:22:24Z)
• Variance-Reduced Off-Policy Memory-Efficient Policy Search [61.23789485979057]
  Off-policy policy optimization is a challenging problem in reinforcement learning. Off-policy algorithms are memory-efficient and capable of learning from off-policy samples.
  arXiv  Detail & Related papers  (2020-09-14T16:22:46Z)
• Robust Reinforcement Learning using Least Squares Policy Iteration with Provable Performance Guarantees [3.8073142980733]
  This paper addresses the problem of model-free reinforcement learning for Robust Markov Decision Process (RMDP) with large state spaces. We first propose the Robust Least Squares Policy Evaluation algorithm, which is a multi-step online model-free learning algorithm for policy evaluation. We then propose Robust Least Squares Policy Iteration (RLSPI) algorithm for learning the optimal robust policy.
  arXiv  Detail & Related papers  (2020-06-20T16:26:50Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.