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The overall performance or expected excess risk of an iterative machine learning algorithm can be decomposed into training error and generalization error. While the former is controlled by its convergence analysis, the latter can be tightly…
We consider the problem of finding optimally stable polynomial approximations to the exponential for application to one-step integration of initial value ordinary and partial differential equations. The objective is to find the largest…
We describe an approach for finding upper bounds on an ODE dynamical system's maximal Lyapunov exponent among all trajectories in a specified set. A minimization problem is formulated whose infimum is equal to the maximal Lyapunov exponent,…
The idea that many important classes of signals can be well-represented by linear combinations of a small set of atoms selected from a given dictionary has had dramatic impact on the theory and practice of signal processing. For practical…
We propose a first-order augmented Lagrangian algorithm (FALC) to solve the composite norm minimization problem min |sigma(F(X)-G)|_alpha + |C(X)- d|_beta subject to A(X)-b in Q; where sigma(X) denotes the vector of singular values of X,…
Many potential applications of reinforcement learning (RL) require guarantees that the agent will perform well in the face of disturbances to the dynamics or reward function. In this paper, we prove theoretically that maximum entropy…
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…
Exponential generalization bounds with near-tight rates have recently been established for uniformly stable learning algorithms. The notion of uniform stability, however, is stringent in the sense that it is invariant to the data-generating…
While modern large-scale datasets often consist of heterogeneous subpopulations -- for example, multiple demographic groups or multiple text corpora -- the standard practice of minimizing average loss fails to guarantee uniformly low losses…
Applying the max-product (and belief-propagation) algorithms to loopy graphs is now quite popular for best assignment problems. This is largely due to their low computational complexity and impressive performance in practice. Still, there…
Finding a representative cohort from a broad pool of candidates is a goal that arises in many contexts such as choosing governing committees and consumer panels. While there are many ways to define the degree to which a cohort represents a…
Temporal logic is a concise way of specifying complex tasks. But motion planning to achieve temporal logic specifications is difficult, and existing methods struggle to scale to complex specifications and high-dimensional system dynamics.…
Maximum entropy distributions with discrete support in $m$ dimensions arise in machine learning, statistics, information theory, and theoretical computer science. While structural and computational properties of max-entropy distributions…
We consider convex and nonconvex constrained optimization with a partially separable objective function: agents minimize the sum of local objective functions, each of which is known only by the associated agent and depends on the variables…
The size of the \textit{smallest suffixient set} of positions of a string recently emerged as a new measure of string \textit{repetitiveness} -- a measure reflecting how much of repetitive content the string contains. We study how to…
Stabilization of graphs has received substantial attention in recent years due to its connection to game theory. Stable graphs are exactly the graphs inducing a matching game with non-empty core. They are also the graphs that induce a…
We study optimization problems that are neither approximable in polynomial time (at least with a constant factor) nor fixed parameter tractable, under widely believed complexity assumptions. Specifically, we focus on Maximum Independent…
Machine learning models are often required to perform well across several pre-defined settings, such as a set of user groups. Worst-case performance is a common metric to capture this requirement, and is the objective of group…
In a regression setting we propose algorithms that reduce the dimensionality of the features while simultaneously maximizing a statistical measure of dependence known as distance correlation between the low-dimensional features and a…
Several fundamental problems that arise in optimization and computer science can be cast as follows: Given vectors $v_1,\ldots,v_m \in \mathbb{R}^d$ and a constraint family ${\cal B}\subseteq 2^{[m]}$, find a set $S \in \cal{B}$ that…