A Generalized Projected Bellman Error for Off-policy Value Estimation in Reinforcement Learning

• URL: http://arxiv.org/abs/2104.13844v3
• Date: Wed, 31 Jul 2024 18:50:28 GMT
• Title: A Generalized Projected Bellman Error for Off-policy Value Estimation in Reinforcement Learning
• Authors: Andrew Patterson, Adam White, Martha White,
• Abstract summary: We introduce a new generalized MSPBE that extends the linear MSPBE to the nonlinear setting. We derive an easy-to-use, but sound, algorithm to minimize the generalized objective.
• Score: 25.39784277231972
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Many reinforcement learning algorithms rely on value estimation, however, the most widely used algorithms -- namely temporal difference algorithms -- can diverge under both off-policy sampling and nonlinear function approximation. Many algorithms have been developed for off-policy value estimation based on the linear mean squared projected Bellman error (MSPBE) and are sound under linear function approximation. Extending these methods to the nonlinear case has been largely unsuccessful. Recently, several methods have been introduced that approximate a different objective -- the mean-squared Bellman error (MSBE) -- which naturally facilitate nonlinear approximation. In this work, we build on these insights and introduce a new generalized MSPBE that extends the linear MSPBE to the nonlinear setting. We show how this generalized objective unifies previous work and obtain new bounds for the value error of the solutions of the generalized objective. We derive an easy-to-use, but sound, algorithm to minimize the generalized objective, and show that it is more stable across runs, is less sensitive to hyperparameters, and performs favorably across four control domains with neural network function approximation.

Related papers

• A Variance Minimization Approach to Temporal-Difference Learning [12.026021568207206]
  This paper introduces a variance minimization (VM) approach for value-based RL instead of error minimization. Based on this approach, we proposed two objectives, the Variance of Bellman Error (VBE) and the Variance of Projected Bellman Error (VPBE)
  arXiv  Detail & Related papers  (2024-11-10T08:56:16Z)
• Agnostic Learning of Mixed Linear Regressions with EM and AM Algorithms [22.79595679373698]
  Mixed linear regression is a well-studied problem in statistics and machine learning. In this paper, we consider the more general problem of learning of mixed linear regression from samples. We show that the AM and EM algorithms lead to learning in mixed linear regression by converging to the population loss minimizers.
  arXiv  Detail & Related papers  (2024-06-03T09:43:24Z)
• Regularized Q-Learning with Linear Function Approximation [2.765106384328772]
  We consider a bi-level optimization formulation of regularized Q-learning with linear functional approximation. We show that, under certain assumptions, the proposed algorithm converges to a stationary point in the presence of Markovian noise.
  arXiv  Detail & Related papers  (2024-01-26T20:45:40Z)
• Hyperparameter Estimation for Sparse Bayesian Learning Models [1.0172874946490507]
  Aparse Bayesian Learning (SBL) models are extensively used in signal processing and machine learning for promoting sparsity through hierarchical priors. This paper presents a framework for the improvement of SBL models for various objective functions. A novel algorithm is introduced showing enhanced efficiency, especially under signal noise ratios.
  arXiv  Detail & Related papers  (2024-01-04T21:24:01Z)
• Multi-objective Reinforcement Learning with Nonlinear Preferences: Provable Approximation for Maximizing Expected Scalarized Return [1.3162012586770577]
  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.
  arXiv  Detail & Related papers  (2023-11-05T02:11:07Z)
• Non-stationary Reinforcement Learning under General Function Approximation [60.430936031067006]
  We first propose a new complexity metric called dynamic Bellman Eluder (DBE) dimension for non-stationary MDPs. Based on the proposed complexity metric, we propose a novel confidence-set based model-free algorithm called SW-OPEA. We show that SW-OPEA is provably efficient as long as the variation budget is not significantly large.
  arXiv  Detail & Related papers  (2023-06-01T16:19:37Z)
• Scalable Bayesian Meta-Learning through Generalized Implicit Gradients [64.21628447579772]
  Implicit Bayesian meta-learning (iBaML) method broadens the scope of learnable priors, but also quantifies the associated uncertainty. Analytical error bounds are established to demonstrate the precision and efficiency of the generalized implicit gradient over the explicit one.
  arXiv  Detail & Related papers  (2023-03-31T02:10:30Z)
• Learning to Estimate Without Bias [57.82628598276623]
  Gauss theorem states that the weighted least squares estimator is a linear minimum variance unbiased estimation (MVUE) in linear models. In this paper, we take a first step towards extending this result to non linear settings via deep learning with bias constraints. A second motivation to BCE is in applications where multiple estimates of the same unknown are averaged for improved performance.
  arXiv  Detail & Related papers  (2021-10-24T10:23:51Z)
• 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)
• Logistic Q-Learning [87.00813469969167]
  We propose a new reinforcement learning algorithm derived from a regularized linear-programming formulation of optimal control in MDPs. The main feature of our algorithm is a convex loss function for policy evaluation that serves as a theoretically sound alternative to the widely used squared Bellman error.
  arXiv  Detail & Related papers  (2020-10-21T17:14:31Z)
• 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)

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.