Saddle Point Optimization for Regret Minimization in Sequential Decision-Making

核心概念

Decision-estimation coefficients optimize exploration-exploitation trade-offs in sequential decision-making.

要約

The content discusses regret minimization in sequential decision-making, focusing on saddle point optimization. It introduces the decision-estimation coefficient (DEC) and its variants, such as the average-constrained DEC. The algorithm ANYTIME-E2D is presented, optimizing the DEC online for structured observations. Connections to information ratio and decoupling coefficient are explored, along with empirical results on linear bandits. Computational aspects and upper bounds are discussed, emphasizing practical implementations.

1. Introduction

   • Regret minimization is crucial in bandits and reinforcement learning.
   • Balancing exploration-exploitation trade-off is key in sequential decision-making.

2. Regret Minimization via Saddle-Point Optimization

   • Sample complexity of regret minimization characterized by min-max programs.
   • Decision-estimation coefficient (DEC) optimizes exploration-exploitation trade-off.
   • Introduction of ANYTIME-E2D algorithm for practical implementation.

3. Related Work

   • Various approaches to regret minimization in bandits and reinforcement learning.
   • Saddle-point problem utilized for optimal regret bounds.

4. Setting

   • Decision-making problem defined with compact decision space Π and observation space O.
   • Models associated with reward functions and observation distributions considered.

5. Regret Minimization via Saddle-Point Optimization

   • Learner aims to minimize gap between decisions under true model f∗.
   • Information function used to quantify statistical evidence against models g ≠ f∗.

6. The Decision-Estimation Coefficient

   • DEC introduced as a min-max game between learner and environment.
   • Constrained DEC parametrized via confidence radius ϵ for online optimization.

7. Anytime Estimation-To-Decisions (Anytime-E2D)

   • E2D algorithm leverages average-constrained DEC for decision-making.
   • Regret bounds derived based on estimation error and worst-case DEC.

8. Certifying Upper Bounds

   • Information ratio and decoupling coefficient used to bound decision-estimation coefficients.

9. Application to Linear Feedback Models

   • Improved regret bounds demonstrated for linear bandits with side-observations.
   • Incremental scheme proposed for iterative computation of sampling distribution.

10. Conclusion

    • ANYTIME-E2D algorithm enhances regret minimization through structured observations.
    • Implementation details provided for finite and linear model classes.

統計

"By reparametrizing the offset DEC with the confidence radius..."
"The learner’s objective is to collect as much reward as possible..."
"The literature studies regret minimization for various objectives..."

引用

"In other words, a learner will inevitably face the exploration-exploitation trade-off where it must balance collecting rewards and collecting information."

抽出されたキーインサイト

Regret Minimization via Saddle Point Optimization

by Joha... 場所 arxiv.org 03-18-2024

https://arxiv.org/pdf/2403.10379.pdf

深掘り質問

How can the concept of saddle point optimization be applied beyond regret minimization

サドルポイント最適化の概念は、後悔最小化以外の領域にも適用することができます。例えば、経済学やゲーム理論などの分野では、異なるエージェント間の競争や協力関係をモデル化する際にサドルポイント最適化が活用されています。また、制御工学や強化学習においても、システムの安定性や性能向上を目指す際にサドルポイント最適化が有効です。さらに、画像処理や信号処理などの分野でも、ノイズ除去や特徴抽出などの問題に対してサドルポイント最適化アプローチが応用されています。

What potential drawbacks or limitations might arise from relying heavily on the decision-estimation coefficient

決定-推定係数（DEC）への依存度が高い場合に生じる可能性のある欠点や制限事項はいくつかあります。まず第一に、「DEC」パラメーターを正確かつ効果的に設定することが困難である場合があります。DECパラメーターは解析から導出された後悔上限値を基準として設定されるため、実際の問題設定で最適な値を見極めることは挑戦的です。さらに、「DEC」アプローチは計算量が多くかかり得るため、実務家から好まれない傾向もあります。

How can the principles discussed in this content be adapted or extended to other fields outside of computer science

このコンテンツで議論された原則は他のコンピューターサイエンス以外の分野でも拡張・応用することが可能です。例えば金融工学ではリスク管理や投資戦略立案時に意思決定支援システムとして利用できますし、医療分野では治療方針策定時など臨床意思決定支援システムとして役立ちます。さらに製造業界では品質管理プロセス改善時等幅広い領域で活用可能です。その他自然言語処理（NLP）、音声認識技術等情報技術以外でも有益性を発揮します。