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Frank-Wolfe algorithms for convex minimization have recently gained considerable attention from the Optimization and Machine Learning communities, as their properties make them a suitable choice in a variety of applications. However, as…
We study optimization algorithms for the finite sum problems frequently arising in machine learning applications. First, we propose novel variants of stochastic gradient descent with a variance reduction property that enables linear…
Planning problems are hard, motion planning, for example, isPSPACE-hard. Such problems are even more difficult in the presence of uncertainty. Although, Markov Decision Processes (MDPs) provide a formal framework for such problems, finding…
A broad class of convex optimization problems can be formulated as a semidefinite program (SDP), minimization of a convex function over the positive-semidefinite cone subject to some affine constraints. The majority of classical SDP solvers…
Multi-stage decision-making under uncertainty, where decisions are taken under sequentially revealing uncertain problem parameters, is often essential to faithfully model managerial problems. Given the significant computational challenges…
Many real-world problems require trading off multiple competing objectives. However, these objectives are often in different units and/or scales, which can make it challenging for practitioners to express numerical preferences over…
This paper explores general multi-robot task and motion planning, where multiple robots in close proximity manipulate objects while satisfying constraints and a given goal. In particular, we formulate the plan refinement problem--which,…
Navigating a collision-free and optimal trajectory for a robot is a challenging task, particularly in environments with moving obstacles such as humans. We formulate this problem as a stochastic optimal control problem. Since solving the…
Determining the most appropriate features for machine learning predictive models is challenging regarding performance and feature acquisition costs. In particular, global feature choice is limited given that some features will only benefit…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
This paper studies a class of multi-robot coordination problems where a team of robots aim to reach their goal regions with minimum time and avoid collisions with obstacles and other robots. A novel numerical algorithm is proposed to…
In this invited contribution, we revisit the stochastic shortest path problem, and show how recent results allow one to improve over the classical solutions: we present algorithms to synthesize strategies with multiple guarantees on the…
Motion planning and control are two core components of the robotic systems autonomy stack. The standard approach to combine these methodologies comprises an offline/open-loop stage, planning, that designs a feasible and safe trajectory to…
We propose a semi-stochastic Frank-Wolfe algorithm with away-steps for regularized empirical risk minimization and extend it to problems with block-coordinate structure. Our algorithms use adaptive step-size and we show that they converge…
Coordinating multiple interacting agents to achieve a common goal is a difficult task with huge applicability. This problem remains hard to solve, even when limiting interactions to be mediated via a static interaction-graph. We present a…
We consider the problem of controlling a Markov decision process (MDP) with a large state space, so as to minimize average cost. Since it is intractable to compete with the optimal policy for large scale problems, we pursue the more modest…
In this work we are interested in stochastic particle methods for multi-objective optimization. The problem is formulated using parametrized, single-objective sub-problems which are solved simultaneously. To this end a consensus based…
The coordinated and efficient distribution of limited resources by individual decisions is a fundamental, unsolved problem. When individuals compete for road capacities, time, space, money, goods, etc., they normally make decisions based on…
This paper addresses the challenge of enabling a single robot to effectively assist multiple humans in decision-making for task planning domains. We introduce a comprehensive framework designed to enhance overall team performance by…
Finding a \emph{single} best solution is the most common objective in combinatorial optimization problems. However, such a single solution may not be applicable to real-world problems as objective functions and constraints are only…