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The minimization of convex functions which are only available through partial and noisy information is a key methodological problem in many disciplines. In this paper we consider convex optimization with noisy zero-th order information,…
Bilevel optimization problems, which are problems where two optimization problems are nested, have more and more applications in machine learning. In many practical cases, the upper and the lower objectives correspond to empirical risk…
We study the intrinsic limitations of sequential convex optimization through the lens of feedback information theory. In the oracle model of optimization, an algorithm queries an {\em oracle} for noisy information about the unknown…
We present a new variant of the secretary problem. Let $A$ be a totally ordered set of $n$ \emph{applicants}. Given $P\subseteq A$ and $x\in A$, let $rr(P,x)=\vert\{z\in P \mid z\leq x\}\vert\mbox{ }$ be the \emph{relative rank of} $x$…
We analyze combinatorial optimization problems with ordinal, i.e., non-additive, objective functions that assign categories (like good, medium and bad) rather than cost coefficients to the elements of feasible solutions. We review different…
We study the prophet secretary problem, a well-studied variant of the classic prophet inequality, where values are drawn from independent known distributions but arrive in uniformly random order. Upon seeing a value at each step, the…
This paper considers the problem of robust adaptive efficient estimating of a periodic function in a continuous time regression model with the dependent noises given by a general square integrable semimartingale with a conditionally…
Stochastic optimization problems often involve data distributions that change in reaction to the decision variables. This is the case for example when members of the population respond to a deployed classifier by manipulating their features…
We study the unconstrained minimization of a smooth and strongly convex population loss function under a stochastic oracle that introduces both additive and multiplicative noise; this is a canonical and widely-studied setting that arises…
Suppose we are given integer $k \leq n$ and $n$ boxes labeled $1,\ldots, n$ by an adversary, each containing a number chosen from an unknown distribution. We have to choose an order to sequentially open these boxes, and each time we open…
Inspired by regularization techniques in statistics and machine learning, we study complementary composite minimization in the stochastic setting. This problem corresponds to the minimization of the sum of a (weakly) smooth function endowed…
Relative to the large literature on upper bounds on complexity of convex optimization, lesser attention has been paid to the fundamental hardness of these problems. Given the extensive use of convex optimization in machine learning and…
We introduce a new method for solving nonlinear continuous optimization problems with chance constraints. Our method is based on a reformulation of the probabilistic constraint as a quantile function. The quantile function is approximated…
We formulate selecting the best optimizing system (SBOS) problems and provide solutions for those problems. In an SBOS problem, a finite number of systems are contenders. Inside each system, a continuous decision variable affects the…
We consider the maximization of a submodular objective function $f:2^U\to\mathbb{R}_{\geq 0}$, where the objective $f$ is not accessed as a value oracle but instead subject to noisy queries. We introduce a versatile adaptive sampling…
The prophet and secretary problems demonstrate online scenarios involving the optimal stopping theory. In a typical prophet or secretary problem, selection decisions are assumed to be immediate and irrevocable. However, many online settings…
The classical algorithms for online learning and decision-making have the benefit of achieving the optimal performance guarantees, but suffer from computational complexity limitations when implemented at scale. More recent sophisticated…
In this work we consider general facility location and social choice problems, in which sets of agents $\mathcal{A}$ and facilities $\mathcal{F}$ are located in a metric space, and our goal is to assign agents to facilities (as well as…
A conditional sampling oracle for a probability distribution D returns samples from the conditional distribution of D restricted to a specified subset of the domain. A recent line of work (Chakraborty et al. 2013 and Cannone et al. 2014)…
We give asymptotic lower bounds of the value for Bruss' optimal stopping problem with multiple stopping chances. It interestingly consists of the asymptotic threshold values in the optimal multiple stopping strategy. Another interesting…