Convex Methods for Constrained Linear Bandits

• URL: http://arxiv.org/abs/2311.04338v2
• Date: Fri, 10 Nov 2023 01:05:55 GMT
• Title: Convex Methods for Constrained Linear Bandits
• Authors: Amirhossein Afsharrad, Ahmadreza Moradipari, Sanjay Lall
• Abstract summary: This work presents a comprehensive study on the computational aspects of safe bandit algorithms, specifically safe linear bandits. We first characterize the properties of the optimal policy for safe linear bandit problem and then propose an end-to-end pipeline of safe linear bandit algorithms.
• Score: 2.5782420501870296
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Recently, bandit optimization has received significant attention in real-world safety-critical systems that involve repeated interactions with humans. While there exist various algorithms with performance guarantees in the literature, practical implementation of the algorithms has not received as much attention. This work presents a comprehensive study on the computational aspects of safe bandit algorithms, specifically safe linear bandits, by introducing a framework that leverages convex programming tools to create computationally efficient policies. In particular, we first characterize the properties of the optimal policy for safe linear bandit problem and then propose an end-to-end pipeline of safe linear bandit algorithms that only involves solving convex problems. We also numerically evaluate the performance of our proposed methods.

Related papers

• Indexed Minimum Empirical Divergence-Based Algorithms for Linear Bandits [55.938644481736446]
  Indexed Minimum Empirical Divergence (IMED) is a highly effective approach to the multi-armed bandit problem. It has been observed to empirically outperform UCB-based algorithms and Thompson Sampling. We present novel linear versions of the IMED algorithm, which we call the family of LinIMED algorithms.
  arXiv  Detail & Related papers  (2024-05-24T04:11:58Z)
• Directional Optimism for Safe Linear Bandits [4.84955052297084]
  The safe linear bandit problem is a version of the classical linear bandit problem where the learner's actions must satisfy an uncertain constraint at all rounds. We find that it is possible to achieve improved regret guarantees for both well-separated problem instances and action sets that are finite star convex sets. Lastly, we introduce a generalization of the safe linear bandit setting where the constraints are convex and adapt our algorithms and analyses to this setting by leveraging a novel convex-analysis based approach.
  arXiv  Detail & Related papers  (2023-08-29T03:54:53Z)
• Accelerating Cutting-Plane Algorithms via Reinforcement Learning Surrogates [49.84541884653309]
  A current standard approach to solving convex discrete optimization problems is the use of cutting-plane algorithms. Despite the existence of a number of general-purpose cut-generating algorithms, large-scale discrete optimization problems continue to suffer from intractability. We propose a method for accelerating cutting-plane algorithms via reinforcement learning.
  arXiv  Detail & Related papers  (2023-07-17T20:11:56Z)
• Log Barriers for Safe Black-box Optimization with Application to Safe Reinforcement Learning [72.97229770329214]
  We introduce a general approach for seeking high dimensional non-linear optimization problems in which maintaining safety during learning is crucial. Our approach called LBSGD is based on applying a logarithmic barrier approximation with a carefully chosen step size. We demonstrate the effectiveness of our approach on minimizing violation in policy tasks in safe reinforcement learning.
  arXiv  Detail & Related papers  (2022-07-21T11:14:47Z)
• Safe Online Bid Optimization with Return-On-Investment and Budget Constraints subject to Uncertainty [87.81197574939355]
  We study the nature of both the optimization and learning problems. We provide an algorithm, namely GCB, guaranteeing sublinear regret at the cost of a potentially linear number of constraints violations. More interestingly, we provide an algorithm, namely GCB_safe(psi,phi), guaranteeing both sublinear pseudo-regret and safety w.h.p. at the cost of accepting tolerances psi and phi.
  arXiv  Detail & Related papers  (2022-01-18T17:24:20Z)
• Optimal Gradient-based Algorithms for Non-concave Bandit Optimization [76.57464214864756]
  This work considers a large family of bandit problems where the unknown underlying reward function is non-concave. Our algorithms are based on a unified zeroth-order optimization paradigm that applies in great generality. We show that the standard optimistic algorithms are sub-optimal by dimension factors.
  arXiv  Detail & Related papers  (2021-07-09T16:04:24Z)
• An Asymptotically Optimal Primal-Dual Incremental Algorithm for Contextual Linear Bandits [129.1029690825929]
  We introduce a novel algorithm improving over the state-of-the-art along multiple dimensions. We establish minimax optimality for any learning horizon in the special case of non-contextual linear bandits.
  arXiv  Detail & Related papers  (2020-10-23T09:12:47Z)
• Reward-Biased Maximum Likelihood Estimation for Linear Stochastic Bandits [16.042075861624056]
  We develop novel index policies that we prove achieve order-optimality, and show that they achieve empirical performance competitive with the state-of-the-art benchmark methods. The new policies achieve this with low time per pull for linear bandits, and thereby resulting in both favorable regret as well as computational efficiency.
  arXiv  Detail & Related papers  (2020-10-08T16:17:53Z)
• Gamification of Pure Exploration for Linear Bandits [34.16123941778227]
  We investigate an active pure-exploration setting, that includes best-arm identification, in the context of linear bandits. Whileally optimal algorithms exist for standard multi-arm bandits, the existence of such algorithms for the best-arm identification in linear bandits has been elusive. We design the first insightally optimal algorithm for fixed-confidence pure exploration in linear bandits.
  arXiv  Detail & Related papers  (2020-07-02T08:20:35Z)
• Bandit algorithms to emulate human decision making using probabilistic distortions [20.422725678982726]
  We formulate two sample multi-armed bandit problems with distorted probabilities on the reward distributions. We consider the aforementioned problems in the regret minimization as well as best arm identification framework for multi-armed bandits.
  arXiv  Detail & Related papers  (2016-11-30T17:37:51Z)

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.