On The Sample Complexity Bounds In Bilevel Reinforcement Learning

• URL: http://arxiv.org/abs/2503.17644v1
• Date: Sat, 22 Mar 2025 04:22:04 GMT
• Title: On The Sample Complexity Bounds In Bilevel Reinforcement Learning
• Authors: Mudit Gaur, Amrit Singh Bedi, Raghu Pasupathu, Vaneet Aggarwal,
• Abstract summary: Bilevel reinforcement learning (BRL) has emerged as a powerful mathematical framework for studying generative AI alignment.<n>We present the first sample complexity result for BRL, achieving a bound of $epsilon-4$.<n>This result extends to standard bilevel optimization problems, providing an interesting theoretical contribution with practical implications.
• Score: 36.239015146313136
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Bilevel reinforcement learning (BRL) has emerged as a powerful mathematical framework for studying generative AI alignment and related problems. While several principled algorithmic frameworks have been proposed, key theoretical foundations, particularly those related to sample complexity, remain underexplored. Understanding and deriving tight sample complexity bounds are crucial for bridging the gap between theory and practice, guiding the development of more efficient algorithms. In this work, we present the first sample complexity result for BRL, achieving a bound of $\epsilon^{-4}$. This result extends to standard bilevel optimization problems, providing an interesting theoretical contribution with practical implications. To address the computational challenges associated with hypergradient estimation in bilevel optimization, we develop a first-order Hessian-free algorithm that does not rely on costly hypergradient computations. By leveraging matrix-free techniques and constrained optimization methods, our approach ensures scalability and practicality. Our findings pave the way for improved methods in AI alignment and other fields reliant on bilevel optimization.

Related papers

• Scalable First-order Method for Certifying Optimal k-Sparse GLMs [9.613635592922174]
  We propose a first-order proximal gradient algorithm to solve the perspective relaxation of the problem within a BnB framework.<n>We show that our approach significantly accelerates dual bound computations and is highly effective in providing optimality certificates for large-scale problems.
  arXiv  Detail & Related papers  (2025-02-13T17:14:18Z)
• qNBO: quasi-Newton Meets Bilevel Optimization [26.0555315825777]
  Bilevel optimization, addressing challenges in hierarchical learning tasks, has gained significant interest in machine learning.<n>We introduce a general framework to address these computational challenges in a coordinated manner.<n>Specifically, we leverage quasi-Newton algorithms to accelerate the resolution of the lower-level problem while efficiently approximating the inverse Hessian-vector product.
  arXiv  Detail & Related papers  (2025-02-03T05:36:45Z)
• Provably Faster Algorithms for Bilevel Optimization via Without-Replacement Sampling [96.47086913559289]
  gradient-based algorithms are widely used in bilevel optimization. We introduce a without-replacement sampling based algorithm which achieves a faster convergence rate. We validate our algorithms over both synthetic and real-world applications.
  arXiv  Detail & Related papers  (2024-11-07T17:05:31Z)
• On the Convergence of Single-Timescale Actor-Critic [49.19842488693726]
  We analyze the global convergence of the single-timescale actor-critic (AC) algorithm for the infinite-horizon discounted Decision Processes (MDs) with finite state spaces.<n>We demonstrate that the step sizes for both the actor and critic must decay as ( O(k-Pfrac12) ) with $k$ diverging from the conventional ( O(k-Pfrac12) ) rates commonly used in (non- optimal) Markov framework optimization.
  arXiv  Detail & Related papers  (2024-10-11T14:46:29Z)
• A Primal-Dual-Assisted Penalty Approach to Bilevel Optimization with Coupled Constraints [66.61399765513383]
  We develop a BLOCC algorithm to tackle BiLevel Optimization problems with Coupled Constraints. We demonstrate its effectiveness on two well-known real-world applications.
  arXiv  Detail & Related papers  (2024-06-14T15:59:36Z)
• Bilevel reinforcement learning via the development of hyper-gradient without lower-level convexity [4.917399520581689]
  Bilevel reinforcement learning (RL) features intertwined two-level problems.<n>Non-level convex information is an impediment to developing bilevel optimization methods.<n>Hyper-gradient serves as an integration of exploitation and exploration.
  arXiv  Detail & Related papers  (2024-05-30T05:24:20Z)
• Moreau Envelope for Nonconvex Bi-Level Optimization: A Single-loop and Hessian-free Solution Strategy [45.982542530484274]
  Large-scale non Bi-Level (BLO) problems are increasingly applied in machine learning. These challenges involve ensuring computational efficiency and providing theoretical guarantees.
  arXiv  Detail & Related papers  (2024-05-16T09:33:28Z)
• Provably Convergent Federated Trilevel Learning [19.15328400013401]
  Trilevel learning, also called trilevel optimization (TLO), has been recognized as a powerful modelling tool for decision process. This paper proposes an asynchronous federated trilevel optimization method to solve TLO problems.
  arXiv  Detail & Related papers  (2023-12-19T04:03:47Z)
• A Generalized Alternating Method for Bilevel Learning under the Polyak-{\L}ojasiewicz Condition [63.66516306205932]
  Bilevel optimization has recently regained interest owing to its applications in emerging machine learning fields. Recent results have shown that simple alternating iteration-based iterations can match interest owing to convex lower-level objective.
  arXiv  Detail & Related papers  (2023-06-04T17:54:11Z)
• DIAMOND: Taming Sample and Communication Complexities in Decentralized Bilevel Optimization [27.317118892531827]
  We develop a new decentralized bilevel optimization called DIAMOND (decentralized single-timescale approximation with momentum and gradient-tracking) We show that the DIAMOND enjoys $mathcalO(epsilon-3/2)$ in sample and communication complexities for achieving an $epsilon$-stationary solution.
  arXiv  Detail & Related papers  (2022-12-05T15:58:00Z)
• Amortized Implicit Differentiation for Stochastic Bilevel Optimization [53.12363770169761]
  We study a class of algorithms for solving bilevel optimization problems in both deterministic and deterministic settings. We exploit a warm-start strategy to amortize the estimation of the exact gradient. By using this framework, our analysis shows these algorithms to match the computational complexity of methods that have access to an unbiased estimate of the gradient.
  arXiv  Detail & Related papers  (2021-11-29T15:10:09Z)
• Faster Algorithm and Sharper Analysis for Constrained Markov Decision Process [56.55075925645864]
  The problem of constrained decision process (CMDP) is investigated, where an agent aims to maximize the expected accumulated discounted reward subject to multiple constraints. A new utilities-dual convex approach is proposed with novel integration of three ingredients: regularized policy, dual regularizer, and Nesterov's gradient descent dual. This is the first demonstration that nonconcave CMDP problems can attain the lower bound of $mathcal O (1/epsilon)$ for all complexity optimization subject to convex constraints.
  arXiv  Detail & Related papers  (2021-10-20T02:57:21Z)
• ES-Based Jacobian Enables Faster Bilevel Optimization [53.675623215542515]
  Bilevel optimization (BO) has arisen as a powerful tool for solving many modern machine learning problems. Existing gradient-based methods require second-order derivative approximations via Jacobian- or/and Hessian-vector computations. We propose a novel BO algorithm, which adopts Evolution Strategies (ES) based method to approximate the response Jacobian matrix in the hypergradient of BO.
  arXiv  Detail & Related papers  (2021-10-13T19:36:50Z)
• Bilevel Optimization for Machine Learning: Algorithm Design and Convergence Analysis [12.680169619392695]
  This thesis provides a comprehensive convergence rate analysis for bilevel optimization algorithms. For the problem-based formulation, we provide a convergence rate analysis for AID- and ITD-based bilevel algorithms. We then develop acceleration bilevel algorithms, for which we provide shaper convergence analysis with relaxed assumptions.
  arXiv  Detail & Related papers  (2021-07-31T22:05:47Z)
• Bilinear Classes: A Structural Framework for Provable Generalization in RL [119.42509700822484]
  Bilinear Classes is a new structural framework which permits generalization in reinforcement learning. The framework incorporates nearly all existing models in which a sample complexity is achievable. Our main result provides an RL algorithm which has sample complexity for Bilinear Classes.
  arXiv  Detail & Related papers  (2021-03-19T16:34:20Z)
• Revisiting the Sample Complexity of Sparse Spectrum Approximation of Gaussian Processes [60.479499225746295]
  We introduce a new scalable approximation for Gaussian processes with provable guarantees which hold simultaneously over its entire parameter space. Our approximation is obtained from an improved sample complexity analysis for sparse spectrum Gaussian processes (SSGPs)
  arXiv  Detail & Related papers  (2020-11-17T05:41:50Z)
• Beyond Worst-Case Analysis in Stochastic Approximation: Moment Estimation Improves Instance Complexity [58.70807593332932]
  We study oracle complexity of gradient based methods for approximation problems. We focus on instance-dependent complexity instead of worst case complexity. Our proposed algorithm and its analysis provide a theoretical justification for the success of moment estimation.
  arXiv  Detail & Related papers  (2020-06-08T09:25:47Z)
• A Generic First-Order Algorithmic Framework for Bi-Level Programming Beyond Lower-Level Singleton [49.23948907229656]
  Bi-level Descent Aggregation is a flexible and modularized algorithmic framework for generic bi-level optimization. We derive a new methodology to prove the convergence of BDA without the LLS condition. Our investigations also demonstrate that BDA is indeed compatible to a verify of particular first-order computation modules.
  arXiv  Detail & Related papers  (2020-06-07T05:18:50Z)

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.