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Designing sample-efficient and computationally feasible reinforcement learning (RL) algorithms is particularly challenging in environments with large or infinite state and action spaces. In this paper, we advance this effort by presenting…

We introduce a geometrically transparent strict saddle property for nonsmooth functions. This property guarantees that simple proximal algorithms on weakly convex problems converge only to local minimizers, when randomly initialized. We…

In this work, we consider a time-varying stochastic saddle point problem in which the objective is revealed sequentially, and the data distribution depends on the decision variables. Problems of this type express the distributional…

Decentralized optimization methods have been in the focus of optimization community due to their scalability, increasing popularity of parallel algorithms and many applications. In this work, we study saddle point problems of sum type,…

We consider power networks in which it is not possible to satisfy all loads at the demand nodes, due to some attack or disturbance to the network. We formulate a model, based on AC power flow equations, to restore the network to feasibility…

Adaptive methods such as Adam and RMSProp are widely used in deep learning but are not well understood. In this paper, we seek a crisp, clean and precise characterization of their behavior in nonconvex settings. To this end, we first…

We consider (stochastic) convex-concave saddle point (SP) problems with high-dimensional decision variables, arising in various applications including machine learning problems. To contend with the challenges in computing full gradients, we…

Reliable obstacle detection and classification in rough and unstructured terrain such as agricultural fields or orchards remains a challenging problem. These environments involve large variations in both geometry and appearance, challenging…

Many modern machine learning applications - from online principal component analysis to covariance matrix identification and dictionary learning - can be formulated as minimization problems on Riemannian manifolds, and are typically solved…

We lower bound the complexity of finding $\epsilon$-stationary points (with gradient norm at most $\epsilon$) using stochastic first-order methods. In a well-studied model where algorithms access smooth, potentially non-convex functions…

We propose and analyze several inexact regularized Newton-type methods for finding a global saddle point of convex-concave unconstrained min-max optimization problems. Compared to first-order methods, our understanding of second-order…

Differentiable simulation is a promising toolkit for fast gradient-based policy optimization and system identification. However, existing approaches to differentiable simulation have largely tackled scenarios where obtaining smooth…

We analyze stochastic gradient algorithms for optimizing nonconvex problems. In particular, our goal is to find local minima (second-order stationary points) instead of just finding first-order stationary points which may be some bad…

Structural learning, a method to estimate the parameters for discrete energy minimization, has been proven to be effective in solving computer vision problems, especially in 3D scene parsing. As the complexity of the models increases,…

Gradient descent is a popular algorithm in optimization, and its performance in convex settings is mostly well understood. In non-convex settings, it has been shown that gradient descent is able to escape saddle points asymptotically and…

A central challenge to using first-order methods for optimizing nonconvex problems is the presence of saddle points. First-order methods often get stuck at saddle points, greatly deteriorating their performance. Typically, to escape from…

Probabilistic sampling methods have become very popular to solve single-shot path planning problems. Rapidly-exploring Random Trees (RRTs) in particular have been shown to be very efficient in solving high dimensional problems. Even though…

We describe a reverse integration approach for the exploration of low-dimensional effective potential landscapes. Coarse reverse integration initialized on a ring of coarse states enables efficient "navigation" on the landscape terrain:…

Robotic systems must be able to quickly and robustly make decisions when operating in uncertain and dynamic environments. While Reinforcement Learning (RL) can be used to compute optimal policies with little prior knowledge about the…

In this paper, we propose and analyze zeroth-order stochastic approximation algorithms for nonconvex and convex optimization, with a focus on addressing constrained optimization, high-dimensional setting and saddle-point avoiding. To handle…