Related papers: Improving and benchmarking of algorithms for decis…

In statistical learning and analysis from shared data, which is increasingly widely adopted in platforms such as federated learning and meta-learning, there are two major concerns: privacy and robustness. Each participating individual…

We develop a regression based primal-dual martingale approach for solving finite time horizon MDPs with general state and action space. As a result, our method allows for the construction of tight upper and lower biased approximations of…

Motivated by, e.g., sensitivity analysis and end-to-end learning, the demand for differentiable optimization algorithms has been significantly increasing. In this paper, we establish a theoretically guaranteed versatile framework that makes…

We revisit a classical assumption for analyzing stochastic gradient algorithms where the squared norm of the stochastic subgradient (or the variance for smooth problems) is allowed to grow as fast as the squared norm of the optimization…

Following a line of work that takes advantage of vast machine-learned data to enhance online algorithms with (possibly erroneous) information about future inputs, we consider predictions in the context of deterministic algorithms for the…

The problem of robust mean estimation in high dimensions is studied, in which a certain fraction (less than half) of the datapoints can be arbitrarily corrupted. Motivated by compressive sensing, the robust mean estimation problem is…

This paper focuses on the online saddle point problem, which involves a sequence of two-player time-varying convex-concave games. Considering the nonstationarity of the environment, we adopt the duality gap and the dynamic Nash equilibrium…

A new relaxed variant of interior point method for low-rank semidefinite programming problems is proposed in this paper. The method is a step outside of the usual interior point framework. In anticipation to converging to a low-rank primal…

We study the fixed-confidence best-arm identification problem in unimodal bandits, in which the means of the arms increase with the index of the arm up to their maximum, then decrease. We derive two lower bounds on the stopping time of any…

Improving algorithms via predictions is a very active research topic in recent years. This paper initiates the systematic study of mechanism design in this model. In a number of well-studied mechanism design settings, we make use of…

We examine online safe multi-agent reinforcement learning using constrained Markov games in which agents compete by maximizing their expected total rewards under a constraint on expected total utilities. Our focus is confined to an episodic…

We establish a simple connection between robust and differentially-private algorithms: private mechanisms which perform well with very high probability are automatically robust in the sense that they retain accuracy even if a constant…

We consider primal-dual pairs of semidefinite programs and assume that they are ill-posed, i.e., both primal and dual are either weakly feasible or weakly infeasible. Under such circumstances, strong duality may break down and the primal…

The problem of constrained Markov decision process is considered. An agent aims to maximize the expected accumulated discounted reward subject to multiple constraints on its costs (the number of constraints is relatively small). A new dual…

We study statistical inference and distributionally robust solution methods for stochastic optimization problems, focusing on confidence intervals for optimal values and solutions that achieve exact coverage asymptotically. We develop a…

In adversarial multi-armed bandits, two performance measures are commonly used: static regret, which compares the learner to the best fixed arm, and dynamic regret, which compares it to the best sequence of arms. While optimal algorithms…

Optimum designs for parameter estimation in generalized regression models are standardly based on the Fisher information matrix (cf. Atkinson et al (2014) for a recent exposition). The corresponding optimality criteria are related to the…

The machine learning literature contains several constructions for prediction intervals that are intuitively reasonable but ultimately ad-hoc in that they do not come with provable performance guarantees. We present methods from the…

Optimization results are one method for understanding neural computation from Nature's perspective and for defining the physical limits on neuron-like engineering. Earlier work looks at individual properties or performance criteria and…

In many domains, worst-case guarantees on the performance (e.g., prediction accuracy) of a decision function subject to distributional shifts and uncertainty about the environment are crucial. In this work we develop a method to quantify…