通过凸优化求解多臂赌博机逆问题，提升计算效率与鲁棒性。
Solving Inverse Problem for Multi-armed Bandits via Convex Optimization
- 利用变量变换将非凸问题转为凸问题，设计两步启发式算法。
- 相比局部优化更稳健，运行时间显著低于蒙特卡洛方法。
- 提供基于CVXPY的易用实现，适合非优化背景用户。
我们研究广泛应用于神经科学和心理学行为建模的多臂赌博机逆问题（IMAB）。首先证明IMAB一般情况下非凸，但可通过变量变换松弛为凸问题。基于此，提出一种两步顺序启发式方法以近似求解IMAB。讨论了在特定条件下该方法可提供全局解并附带证明证书，同时提出近似策略以进一步降低计算时间。数值实验表明，该启发式方法比重复局部优化更鲁棒，且在显著减少运行时间的情况下达到蒙特卡洛方法的性能。我们基于CVXPY提供了方法实现，便于不熟悉凸优化的用户直接应用。
原文摘要 · Abstract (English)
We consider the inverse problem of multi-armed bandits (IMAB) that are widely used in neuroscience and psychology research for behavior modelling. We first show that the IMAB problem is not convex in general, but can be relaxed to a convex problem via variable transformation. Based on this result, we propose a two-step sequential heuristic for (approximately) solving the IMAB problem. We discuss a condition where our method provides global solution to the IMAB problem with certificate, as well as approximations to further save computing time. Numerical experiments indicate that our heuristic method is more robust than directly solving the IMAB problem via repeated local optimization, and can achieve the performance of Monte Carlo methods within a significantly decreased running time. We provide the implementation of our method based on CVXPY, which allows straightforward application by users not well versed in convex optimization.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。