Multi-objective Reinforcement Learning with Nonlinear Preferences: Provable Approximation for Maximizing Expected Scalarized Return

• URL: http://arxiv.org/abs/2311.02544v3
• Date: Wed, 25 Sep 2024 18:57:14 GMT
• Title: Multi-objective Reinforcement Learning with Nonlinear Preferences: Provable Approximation for Maximizing Expected Scalarized Return
• Authors: Nianli Peng, Muhang Tian, Brandon Fain,
• Abstract summary: We study multi-objective reinforcement learning with nonlinear preferences over trajectories. We derive an extended form of Bellman optimality for nonlinear optimization. We show that there can be a substantial gap between the optimal policy computed by our algorithm and alternative baselines.
• Score: 1.3162012586770577
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: We study multi-objective reinforcement learning with nonlinear preferences over trajectories. That is, we maximize the expected value of a nonlinear function over accumulated rewards (expected scalarized return or ESR) in a multi-objective Markov Decision Process (MOMDP). We derive an extended form of Bellman optimality for nonlinear optimization that explicitly considers time and current accumulated reward. Using this formulation, we describe an approximation algorithm for computing an approximately optimal non-stationary policy in pseudopolynomial time for smooth scalarization functions with a constant number of rewards. We prove the approximation analytically and demonstrate the algorithm experimentally, showing that there can be a substantial gap between the optimal policy computed by our algorithm and alternative baselines.

Related papers

• Pessimistic Nonlinear Least-Squares Value Iteration for Offline Reinforcement Learning [53.97335841137496]
  We propose an oracle-efficient algorithm, dubbed Pessimistic Least-Square Value Iteration (PNLSVI) for offline RL with non-linear function approximation. Our algorithm enjoys a regret bound that has a tight dependency on the function class complexity and achieves minimax optimal instance-dependent regret when specialized to linear function approximation.
  arXiv  Detail & Related papers  (2023-10-02T17:42:01Z)
• Inference on Optimal Dynamic Policies via Softmax Approximation [27.396891119011215]
  We show that a simple soft-max approximation to the optimal treatment regime can achieve valid inference on the truly optimal regime. Our work combines techniques from semi-parametric inference and $g$-estimation, together with an appropriate array central limit theorem.
  arXiv  Detail & Related papers  (2023-03-08T07:42:47Z)
• 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)
• Sparse high-dimensional linear regression with a partitioned empirical Bayes ECM algorithm [62.997667081978825]
  We propose a computationally efficient and powerful Bayesian approach for sparse high-dimensional linear regression. Minimal prior assumptions on the parameters are used through the use of plug-in empirical Bayes estimates. The proposed approach is implemented in the R package probe.
  arXiv  Detail & Related papers  (2022-09-16T19:15:50Z)
• Variance-Aware Off-Policy Evaluation with Linear Function Approximation [85.75516599931632]
  We study the off-policy evaluation problem in reinforcement learning with linear function approximation. We propose an algorithm, VA-OPE, which uses the estimated variance of the value function to reweight the Bellman residual in Fitted Q-Iteration.
  arXiv  Detail & Related papers  (2021-06-22T17:58:46Z)
• Sparse Bayesian Learning via Stepwise Regression [1.2691047660244335]
  We propose a coordinate ascent algorithm for SBL termed Relevance Matching Pursuit (RMP) As its noise variance parameter goes to zero, RMP exhibits a surprising connection to Stepwise Regression. We derive novel guarantees for Stepwise Regression algorithms, which also shed light on RMP.
  arXiv  Detail & Related papers  (2021-06-11T00:20:27Z)
• Provably Correct Optimization and Exploration with Non-linear Policies [65.60853260886516]
  ENIAC is an actor-critic method that allows non-linear function approximation in the critic. We show that under certain assumptions, the learner finds a near-optimal policy in $O(poly(d))$ exploration rounds. We empirically evaluate this adaptation and show that it outperforms priors inspired by linear methods.
  arXiv  Detail & Related papers  (2021-03-22T03:16:33Z)
• Stochastic Learning Approach to Binary Optimization for Optimal Design of Experiments [0.0]
  We present a novel approach to binary optimization for optimal experimental design (OED) for Bayesian inverse problems governed by mathematical models such as partial differential equations. The OED utility function, namely, the regularized optimality gradient, is cast into an objective function in the form of an expectation over a Bernoulli distribution. The objective is then solved by using a probabilistic optimization routine to find an optimal observational policy.
  arXiv  Detail & Related papers  (2021-01-15T03:54:12Z)
• A maximum-entropy approach to off-policy evaluation in average-reward MDPs [54.967872716145656]
  This work focuses on off-policy evaluation (OPE) with function approximation in infinite-horizon undiscounted Markov decision processes (MDPs) We provide the first finite-sample OPE error bound, extending existing results beyond the episodic and discounted cases. We show that this results in an exponential-family distribution whose sufficient statistics are the features, paralleling maximum-entropy approaches in supervised learning.
  arXiv  Detail & Related papers  (2020-06-17T18:13:37Z)

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.