Regret-optimal measurement-feedback control

鲁棒遗憾最优控制

Robust Regret Optimal Control

本文提出一种基于鲁棒$H_\infty$性能条件的鲁棒遗憾最优控制综合方法，通过DK迭代设计控制器，并在三个示例中验证其优于不考虑不确定性的遗憾最优控制器。

Optimal exploration strategies for finite horizon regret minimization in some adaptive control problems

In this work, we consider the problem of regret minimization in adaptive minimum variance and linear quadratic control problems. Regret minimization has been extensively studied in the literature for both types of adaptive control problems. Most of these works give results of the optimal rate of the regret in the asymptotic regime. In the minimum variance case, the optimal asymptotic rate for the regret is $\log(T)$ which can be reached without any additional external excitation. On the contrary, for most adaptive linear quadratic problems, it is necessary to add an external excitation in orde…

A System Level Approach to Regret Optimal Control

We present an optimisation-based method for synthesising a dynamic regret optimal controller for linear systems with potentially adversarial disturbances and known or adversarial initial conditions. The dynamic regret is defined as the difference between the true incurred cost of the system and the cost which could have optimally been achieved under any input sequence having full knowledge of all future disturbances for a given disturbance energy. This problem formulation can be seen as an alternative to classical $\mathcal{H}_2$- or $\mathcal{H}_\infty$-control. The proposed controller synthe…

Regret-optimal control in dynamic environments

We consider control in linear time-varying dynamical systems from the perspective of regret minimization. Unlike most prior work in this area, we focus on the problem of designing an online controller which minimizes regret against the best dynamic sequence of control actions selected in hindsight (dynamic regret), instead of the best fixed controller in some specific class of controllers (static regret). This formulation is attractive when the environment changes over time and no single controller achieves good performance over the entire time horizon. We derive the state-space structure of t…

部分可观测下的遗憾最优控制

Regret-Optimal Control under Partial Observability

本文研究部分可观测系统下的遗憾最优控制，扩展了全信息框架至测量反馈场景，推导显式状态空间解并验证实用性。

在平均奖励MDPs中实现可处理的最小极大最优遗憾

Achieving Tractable Minimax Optimal Regret in Average Reward MDPs

针对平均奖励MDPs中现有算法遗憾次优或计算低效的问题，提出首个无需先验信息且具有最小极大最优遗憾的可处理算法，并利用PMEVI子程序计算偏置约束策略以改进多种算法的遗憾界。

基于基线的安全输出反馈改进

Safe Output Feedback Improvement with Baselines

针对数据驱动控制中极小极大方法过于保守的问题，提出基于基线遗憾的两步输出反馈控制设计方法，通过凸近似与场景方法高效求解，有效提升了控制器性能并降低了方差。