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A common pursuit in modern statistical learning is to attain satisfactory generalization out of the source data distribution (OOD). In theory, the challenge remains unsolved even under the canonical setting of covariate shift for the linear…
We propose a simple, scalable, and fast gradient descent algorithm to optimize a nonconvex objective for the rank minimization problem and a closely related family of semidefinite programs. With $O(r^3 \kappa^2 n \log n)$ random…
Sequential change-point detection when the distribution parameters are unknown is a fundamental problem in statistics and machine learning. When the post-change parameters are unknown, we consider a set of detection procedures based on…
Low-rank regularization (LRR) has been widely applied in various machine learning tasks, but the associated optimization is challenging. Directly optimizing the rank function under constraints is NP-hard in general. To overcome this…
In the contextual linear bandit setting, algorithms built on the optimism principle fail to exploit the structure of the problem and have been shown to be asymptotically suboptimal. In this paper, we follow recent approaches of deriving…
We propose a sample-efficient alternative for importance weighting for situations where one only has sample access to the probability distribution that generates the observations. Our new method, called Geometric Resampling (GR), is…
Recent works have shown that gradient-update alignment is a powerful signal for modulating optimizer updates, often leading to faster training. We promote this update-wise heuristic as a mathematically grounded principle for selecting and…
Gradient-based approaches to direct policy search in reinforcement learning have received much recent attention as a means to solve problems of partial observability and to avoid some of the problems associated with policy degradation in…
There have been many recent advances on provably efficient Reinforcement Learning (RL) in problems with rich observation spaces. However, all these works share a strong realizability assumption about the optimal value function of the true…
We study the $\ell_0$-Low Rank Approximation Problem, where the goal is, given an $m \times n$ matrix $A$, to output a rank-$k$ matrix $A'$ for which $\|A'-A\|_0$ is minimized. Here, for a matrix $B$, $\|B\|_0$ denotes the number of its…
We develop two iterative algorithms for solving the low rank phase retrieval (LRPR) problem. LRPR refers to recovering a low-rank matrix $\X$ from magnitude-only (phaseless) measurements of random linear projections of its columns. Both…
In this work, we propose an alternating low-rank decomposition (ALRD) approach and novel subspace algorithms for direction-of-arrival (DOA) estimation. In the ALRD scheme, the decomposition matrix for rank reduction is composed of a set of…
Randomized rankings have been of recent interest to achieve ex-ante fairer exposure and better robustness than deterministic rankings. We propose a set of natural axioms for randomized group-fair rankings and prove that there exists a…
We establish novel generalization bounds for learning algorithms that converge to global minima. We do so by deriving black-box stability results that only depend on the convergence of a learning algorithm and the geometry around the…
In this paper, we propose and study opportunistic reinforcement learning - a new variant of reinforcement learning problems where the regret of selecting a suboptimal action varies under an external environmental condition known as the…
Consensus optimization enables autonomous agents to solve joint tasks through peer-to-peer exchanges alone. Classical decentralized gradient descent is appealing for its minimal state but fails to achieve exact consensus with fixed…
Recently, Musco and Woodruff (FOCS, 2017) showed that given an $n \times n$ positive semidefinite (PSD) matrix $A$, it is possible to compute a $(1+\epsilon)$-approximate relative-error low-rank approximation to $A$ by querying…
An algorithm for unconstrained non-convex optimization is described, which does not evaluate the objective function and in which minimization is carried out, at each iteration, within a randomly selected subspace. It is shown that this…
We study the first-order convex optimization problem, where we have black-box access to a (not necessarily smooth) function $f:\mathbb{R}^n \to \mathbb{R}$ and its (sub)gradient. Our goal is to find an $\epsilon$-approximate minimum of $f$…
Reinforcement learning lies at the intersection of several challenges. Many applications of interest involve extremely large state spaces, requiring function approximation to enable tractable computation. In addition, the learner has only a…