Algorithms for offline bandits must optimize decisions in uncertain
environments using only offline data. A compelling and increasingly popular
objective in offline bandits is to learn a policy which achieves low Bayesian
regret with high confidence. An appealing approach to this problem, inspired by
recent offline reinforcement learning results, is to maximize a form of lower
confidence bound (LCB). This paper proposes a new approach that directly
minimizes upper bounds on Bayesian regret using efficient conic optimization
solvers. Our bounds build on connections among Bayesian regret, Value-at-Risk
(VaR), and chance-constrained optimization. Compared to prior work, our
algorithm attains superior theoretical offline regret bounds and better results
in numerical simulations. Finally, we provide some evidence that popular
LCB-style algorithms may be unsuitable for minimizing Bayesian regret in
offline bandits.

本文提出了一种利用高效对偶锥优化器，直接最小化贝叶斯遗憾的上界以及与 VaR 和机遇约束优化之间的关系建立的边界的新方法来优化不确定环境下离线数据的决策问题，并与现有算法进行了比较。

离线赌博机中基于贝叶斯遗憾最小化的凸松弛方法

A Convex Relaxation Approach to Bayesian Regret Minimization in Offline  Bandits

Oversubscription is a common practice for improving cloud resource
utilization. It allows the cloud service provider to sell more resources than
the physical limit, assuming not all users would fully utilize the resources
simultaneously. However, how to design an oversubscription policy that improves
utilization while satisfying the some safety constraints remains an open
problem. Existing methods and industrial practices are over-conservative,
ignoring the coordination of diverse resource usage patterns and probabilistic
constraints. To address these two limitations, this paper formulates the
oversubscription for cloud as a chance-constrained optimization problem and
propose an effective Chance Constrained Multi-Agent Reinforcement Learning
(C2MARL) method to solve this problem. Specifically, C2MARL reduces the number
of constraints by considering their upper bounds and leverages a multi-agent
reinforcement learning paradigm to learn a safe and optimal coordination
policy. We evaluate our C2MARL on an internal cloud platform and public cloud
datasets. Experiments show that our C2MARL outperforms existing methods in
improving utilization ($20\%\sim 86\%$) under different levels of safety
constraints.

本文针对云服务商超额订阅资源的使用问题，提出了一种基于概率约束优化和多智能体强化学习的超额订阅策略，实验表明该方法可以在不同安全约束条件下提高资源利用率 (20%~86%)。

机会约束多智能体强化学习中的云计算合作超额订阅学习

Learning Cooperative Oversubscription for Cloud by Chance-Constrained Multi-Agent Reinforcement Learning

The concepts of risk-aversion, chance-constrained optimization, and robust
optimization have developed significantly over the last decade. Statistical
learning community has also witnessed a rapid theoretical and applied growth by
relying on these concepts. A modeling framework, called distributionally robust
optimization (DRO), has recently received significant attention in both the
operations research and statistical learning communities. This paper surveys
main concepts and contributions to DRO, and its relationships with robust
optimization, risk-aversion, chance-constrained optimization, and function
regularization.

本文概述了分布鲁棒优化（DRO）的主要概念和贡献，以及它与鲁棒优化、风险规避、机会约束优化和函数正则化的关系。

分布鲁棒优化：一篇综述

Distributionally Robust Optimization: A Review

Can we conclude the stability of an unknown dynamical system from the
knowledge of a finite number of snapshots of trajectories? We tackle this
black-box problem for switched linear systems. We show that, for any given
random set of observations, one can give probabilistic stability guarantees.
The probabilistic nature of these guarantees implies a trade-off between their
quality and the desired level of confidence. We provide an explicit way of
computing the best stability-like guarantee, as a function of both the number
of observations and the required level of confidence. Our proof techniques rely
on geometrical analysis, chance-constrained optimization, and stability
analysis tools for switched systems, including the joint spectral radius.

对于未知动态系统与开关线性系统，我们通过几何分析、机会限制优化和联合谱半径等稳定性分析工具，可以在有限的观测数基础上给出概率上的稳定性保证，并提供了计算最佳稳定性保证的方法，可以平衡保证质量和置信水平。