Spectral Decomposition Representation for Reinforcement Learning

• URL: http://arxiv.org/abs/2208.09515v1
• Date: Fri, 19 Aug 2022 19:01:30 GMT
• Title: Spectral Decomposition Representation for Reinforcement Learning
• Authors: Tongzheng Ren, Tianjun Zhang, Lisa Lee, Joseph E. Gonzalez, Dale Schuurmans, Bo Dai
• Abstract summary: We propose an alternative spectral method, Spectral Decomposition Representation (SPEDER), that extracts a state-action abstraction from the dynamics without inducing spurious dependence on the data collection policy. A theoretical analysis establishes the sample efficiency of the proposed algorithm in both the online and offline settings. An experimental investigation demonstrates superior performance over current state-of-the-art algorithms across several benchmarks.
• Score: 100.0424588013549
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Representation learning often plays a critical role in reinforcement learning by managing the curse of dimensionality. A representative class of algorithms exploits a spectral decomposition of the stochastic transition dynamics to construct representations that enjoy strong theoretical properties in an idealized setting. However, current spectral methods suffer from limited applicability because they are constructed for state-only aggregation and derived from a policy-dependent transition kernel, without considering the issue of exploration. To address these issues, we propose an alternative spectral method, Spectral Decomposition Representation (SPEDER), that extracts a state-action abstraction from the dynamics without inducing spurious dependence on the data collection policy, while also balancing the exploration-versus-exploitation trade-off during learning. A theoretical analysis establishes the sample efficiency of the proposed algorithm in both the online and offline settings. In addition, an experimental investigation demonstrates superior performance over current state-of-the-art algorithms across several benchmarks.

Related papers

• Spectral Estimators for Multi-Index Models: Precise Asymptotics and Optimal Weak Recovery [21.414505380263016]
  We focus on recovering the subspace spanned by the signals via spectral estimators. Our main technical contribution is a precise characterization of the performance of spectral methods. Our analysis unveils a phase transition phenomenon in which, as the sample complexity grows, eigenvalues escape from the bulk of the spectrum.
  arXiv  Detail & Related papers  (2025-02-03T18:08:30Z)
• ResKoopNet: Learning Koopman Representations for Complex Dynamics with Spectral Residuals [1.8570740863168362]
  Existing methods for approximating Koopman operator's spectral components often suffer from theoretical limitations. We introduce ResKoopNet, a novel method that explicitly minimizes the spectral residual to compute Koopman eigenpairs. Experiments on physical and biological systems demonstrate ResKoopNet's superior accuracy in spectral approximation compared to existing methods.
  arXiv  Detail & Related papers  (2025-01-01T02:19:42Z)
• Nonstationary Sparse Spectral Permanental Process [24.10531062895964]
  We propose a novel approach utilizing the sparse spectral representation of nonstationary kernels. This technique relaxes the constraints on kernel types and stationarity, allowing for more flexible modeling. Experimental results on both synthetic and real-world datasets demonstrate the effectiveness of our approach.
  arXiv  Detail & Related papers  (2024-10-04T16:40:56Z)
• Learned Regularization for Inverse Problems: Insights from a Spectral Model [1.4963011898406866]
  This chapter provides a theoretically founded investigation of state-of-the-art learning approaches for inverse problems. We give an extended definition of regularization methods and their convergence in terms of the underlying data distributions.
  arXiv  Detail & Related papers  (2023-12-15T14:50:14Z)
• Latent Variable Representation for Reinforcement Learning [131.03944557979725]
  It remains unclear theoretically and empirically how latent variable models may facilitate learning, planning, and exploration to improve the sample efficiency of model-based reinforcement learning. We provide a representation view of the latent variable models for state-action value functions, which allows both tractable variational learning algorithm and effective implementation of the optimism/pessimism principle. In particular, we propose a computationally efficient planning algorithm with UCB exploration by incorporating kernel embeddings of latent variable models.
  arXiv  Detail & Related papers  (2022-12-17T00:26:31Z)
• Reinforcement Learning from Partial Observation: Linear Function Approximation with Provable Sample Efficiency [111.83670279016599]
  We study reinforcement learning for partially observed decision processes (POMDPs) with infinite observation and state spaces. We make the first attempt at partial observability and function approximation for a class of POMDPs with a linear structure.
  arXiv  Detail & Related papers  (2022-04-20T21:15:38Z)
• Deep Equilibrium Assisted Block Sparse Coding of Inter-dependent Signals: Application to Hyperspectral Imaging [71.57324258813675]
  A dataset of inter-dependent signals is defined as a matrix whose columns demonstrate strong dependencies. A neural network is employed to act as structure prior and reveal the underlying signal interdependencies. Deep unrolling and Deep equilibrium based algorithms are developed, forming highly interpretable and concise deep-learning-based architectures.
  arXiv  Detail & Related papers  (2022-03-29T21:00:39Z)
• A Free Lunch from the Noise: Provable and Practical Exploration for Representation Learning [55.048010996144036]
  We show that under some noise assumption, we can obtain the linear spectral feature of its corresponding Markov transition operator in closed-form for free. We propose Spectral Dynamics Embedding (SPEDE), which breaks the trade-off and completes optimistic exploration for representation learning by exploiting the structure of the noise.
  arXiv  Detail & Related papers  (2021-11-22T19:24:57Z)
• Discrete Action On-Policy Learning with Action-Value Critic [72.20609919995086]
  Reinforcement learning (RL) in discrete action space is ubiquitous in real-world applications, but its complexity grows exponentially with the action-space dimension. We construct a critic to estimate action-value functions, apply it on correlated actions, and combine these critic estimated action values to control the variance of gradient estimation. These efforts result in a new discrete action on-policy RL algorithm that empirically outperforms related on-policy algorithms relying on variance control techniques.
  arXiv  Detail & Related papers  (2020-02-10T04:23:09Z)

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.