Related papers: A Novel Robust Approach to Least Squares Problems …
Least worst regret (and sometimes minimax) analysis are often used for decision making whenever it is difficult, or inappropriate, to attach probabilities to possible future scenarios. We show that, for each of these two approaches and…
We provide a unified treatment of a broad class of noisy structure recovery problems, known as structured normal means problems. In this setting, the goal is to identify, from a finite collection of Gaussian distributions with different…
Due to the COVID-19 pandemic, there is an increasing demand for portable CT machines worldwide in order to diagnose patients in a variety of settings. This has led to a need for CT image reconstruction algorithms that can produce high…
We consider the setting of online linear regression for arbitrary deterministic sequences, with the square loss. We are interested in the aim set by Bartlett et al. (2015): obtain regret bounds that hold uniformly over all competitor…
It is increasingly common to solve combinatorial optimisation problems that are partially-specified. We survey the case where the objective function or the relations between variables are not known or are only partially specified. The…
Performance of adaptive control policies is assessed through the regret with respect to the optimal regulator, which reflects the increase in the operating cost due to uncertainty about the dynamics parameters. However, available results in…
In this paper, we consider an adaptive approach to address optimization problems with uncertain cost parameters. Here, the decision maker selects an initial decision, observes the realization of the uncertain cost parameters, and then is…
In this work, we investigate data fitting problems with random noises. A randomized progressive iterative regularization method is proposed. It works well for large-scale matrix computations and converges in expectation to the least-squares…
Towards bridging classical optimal control and online learning, regret minimization has recently been proposed as a control design criterion. This competitive paradigm penalizes the loss relative to the optimal control actions chosen by a…
We study a broad class of assortment optimization problems in an offline and data-driven setting. In such problems, a firm lacks prior knowledge of the underlying choice model, and aims to determine an optimal assortment based on historical…
We investigate the problem of continuous-time causal estimation under a minimax criterion. Let $X^T = \{X_t,0\leq t\leq T\}$ be governed by the probability law $P_{\theta}$ from a class of possible laws indexed by $\theta \in \Lambda$, and…
The efficacy of robust optimization spans a variety of settings with uncertainties bounded in predetermined sets. In many applications, uncertainties are affected by decisions and cannot be modeled with current frameworks. This paper takes…
Kalman and H-infinity filters, the most popular paradigms for linear state estimation, are designed for very specific specific noise and disturbance patterns, which may not appear in practice. State observers based on the minimization of…
Minimax lower bounds are pessimistic in nature: for any given estimator, minimax lower bounds yield the existence of a worst-case target vector $\beta^*_{worst}$ for which the prediction error of the given estimator is bounded from below.…
We revisit online binary classification by shifting the focus from competing with the best-in-class binary loss to competing against relaxed benchmarks that capture smoothed notions of optimality. Instead of measuring regret relative to the…
In this paper we focus on the unconstrained binary quadratic optimization model, maximize x^t Qx, x binary, and consider the problem of identifying optimal solutions that are robust with respect to perturbations in the Q matrix.. We are…
Meaningful comparison between sets of observations often necessitates alignment or registration between them, and the resulting optimization problems range in complexity from those admitting simple closed-form solutions to those requiring…
We study online learning problems in which a decision maker has to take a sequence of decisions subject to $m$ long-term constraints. The goal of the decision maker is to maximize their total reward, while at the same time achieving small…
We consider robust shortest path problems, where the aim is to find a path that optimizes the worst-case performance over an uncertainty set containing all relevant scenarios for arc costs. The usual approach for such problems is to assume…
This guide provides a reference for high-probability regret bounds in empirical risk minimization (ERM). The presentation is modular: we begin with intuition and general proof strategies, then state broadly applicable guarantees under…