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We revisit the Frank-Wolfe (FW) optimization under strongly convex constraint sets. We provide a faster convergence rate for FW without line search, showing that a previously overlooked variant of FW is indeed faster than the standard…

Inverse reinforcement learning aims to infer the reward function that explains expert behavior observed through trajectories of state--action pairs. A long-standing difficulty in classical IRL is the non-uniqueness of the recovered reward:…

An adaptive regularization algorithm for unconstrained nonconvex optimization is presented in which the objective function is never evaluated, but only derivatives are used. This algorithm belongs to the class of adaptive regularization…

Motivated by recent increased interest in optimization algorithms for non-convex optimization in application to training deep neural networks and other optimization problems in data analysis, we give an overview of recent theoretical…

We present a new approach for computing approximate global minimizers to a large class of non-local pairwise interaction problems defined over probability distributions. The approach predicts candidate global minimizers, with a recovery…

An adaptive regularization algorithm for unconstrained nonconvex optimization is proposed that is capable of handling inexact objective-function and derivative values, and also of providing approximate minimizer of arbitrary order. In…

We study unconstrained optimization problems with nonsmooth and convex objective function in the form of a mathematical expectation. The proposed method approximates the expected objective function with a sample average function using…

We introduce a quadratically-constrained approximation (QCAC) of the AC optimal power flow (AC-OPF) problem. Unlike existing approximations like the DC-OPF, our model does not rely on typical assumptions such as high reactance-to-resistance…

In this paper, we propose a successive convex approximation framework for sparse optimization where the nonsmooth regularization function in the objective function is nonconvex and it can be written as the difference of two convex…

We show that a certain entropy-like function is convex, under an optimal transport problem that is adapted to Ricci flow. We use this to reprove the monotonicity of Perelman's reduced volume.

We consider the problem of function approximation by two-layer neural nets with random weights that are "nearly Gaussian" in the sense of Kullback-Leibler divergence. Our setting is the mean-field limit, where the finite population of…

This paper focuses on finding approximate solutions to stochastic optimal control problems with control domains being not necessarily convex, where the state trajectory is subject to controlled stochastic differential equations. The…

Reinforcement learning (RL) is an important field of research in machine learning that is increasingly being applied to complex optimization problems in physics. In parallel, concepts from physics have contributed to important advances in…

Gradient flows are a powerful tool for optimizing functionals in general metric spaces, including the space of probabilities endowed with the Wasserstein metric. A typical approach to solving this optimization problem relies on its…

In this work, we investigate a stochastic control framework for global optimization over both Euclidean spaces and the Wasserstein space of probability measures, where the objective function may be non-convex and/or non-differentiable. In…

In this paper, we consider reinforcement learning of nonlinear systems with continuous state and action spaces. We present an episodic learning algorithm, where we for each episode use convex optimization to find a two-layer neural network…

In this work, we propose a novel inverse reinforcement learning (IRL) algorithm for constrained Markov decision process (CMDP) problems. In standard IRL problems, the inverse learner or agent seeks to recover the reward function of the MDP,…

We study nonconvex distributed optimization in multi-agent networks with time-varying (nonsymmetric) connectivity. We introduce the first algorithmic framework for the distributed minimization of the sum of a smooth (possibly nonconvex and…

This paper studies the connections between mean-field games and the social welfare optimization problems. We consider a mean field game in functional spaces with a large population of agents, each of which seeks to minimize an individual…

This paper focuses on stochastic proximal gradient methods for optimizing a smooth non-convex loss function with a non-smooth non-convex regularizer and convex constraints. To the best of our knowledge we present the first non-asymptotic…