Related papers: Combining Progressive Hedging with a Frank-Wolfe M…

We develop a novel stochastic primal dual splitting method with Bregman distances for solving a structured composite problems involving infimal convolutions in non-Euclidean spaces. The sublinear convergence in expectation of the…

In this paper, we consider a Model Predictive Control (MPC) problem of a continuous-time linear time-invariant system subject to continuous-time path constraints on the states and the inputs. By leveraging the concept of differential…

We propose \textit{DeepMartingale}, a deep-learning framework for the dual formulation of discrete-monitoring optimal stopping problems under continuous-time models. Leveraging a martingale representation, our method implements a…

We consider stochastic strongly-convex-strongly-concave (SCSC) saddle point (SP) problems which frequently arise in applications ranging from distributionally robust learning to game theory and fairness in machine learning. We focus on the…

In distributed machine learning, efficient training across multiple agents with different data distributions poses significant challenges. Even with a centralized coordinator, current algorithms that achieve optimal communication complexity…

Necessary optimality conditions in Lagrangian form and the sequential minimization framework are extended to mixed-integer nonlinear optimization, without any convexity assumptions. Building upon a recently developed notion of local…

The Frank-Wolfe algorithm has seen a resurgence in popularity due to its ability to efficiently solve constrained optimization problems in machine learning and high-dimensional statistics. As such, there is much interest in establishing…

Risk-aware control, though with promise to tackle unexpected events, requires a known exact dynamical model. In this work, we propose a model-free framework to learn a risk-aware controller with a focus on the linear system. We formulate it…

This work proposes a new algorithm for training a re-weighted L2 Support Vector Machine (SVM), inspired on the re-weighted Lasso algorithm of Cand\`es et al. and on the equivalence between Lasso and SVM shown recently by Jaggi. In…

Recent observations have been made that bridge splitting methods arising from optimization, to the Hopf and Lax formulas for Hamilton-Jacobi Equations with Hamiltonians $H(p)$. This has produced extremely fast algorithms in computing…

This paper studies a classic maximum entropy sampling problem (MESP), which aims to select the most informative principal submatrix of a prespecified size from a covariance matrix. MESP has been widely applied to many areas, including…

We study entropy-regularized constrained Markov decision processes (CMDPs) under the soft-max parameterization, in which an agent aims to maximize the entropy-regularized value function while satisfying constraints on the expected total…

We develop an efficient method for solving non-convex constrained optimization problems that are pervasive in economics. The optimal solution to these problems often involves randomization. We employ a Lagrangian framework and prove that…

Consider the minimization of a nonconvex differentiable function over a polyhedron. A popular primal-dual first-order method for this problem is to perform a gradient projection iteration for the augmented Lagrangian function and then…

Safety is essential for reinforcement learning (RL) applied in real-world tasks like autonomous driving. Chance constraints which guarantee the satisfaction of state constraints at a high probability are suitable to represent the…

In this paper, we consider the linear programming (LP) formulation for deep reinforcement learning. The number of the constraints depends on the size of state and action spaces, which makes the problem intractable in large or continuous…

We present a new kind of Lagrangian duality theory for set-valued convex optimization problems whose objective and constraint maps are defined between preordered normed spaces. The theory is accomplished by introducing a new set-valued…

This paper is concerned with augmented Lagrangian methods for the treatment of fully convex composite optimization problems. We extend the classical relationship between augmented Lagrangian methods and the proximal point algorithm to the…

This paper deals with supervised classification and feature selection in high dimensional space. A classical approach is to project data on a low dimensional space and classify by minimizing an appropriate quadratic cost. A strict control…

In this paper we propose a general framework to characterize and solve the stochastic optimization problems with multiple objectives underlying many real world learning applications. We first propose a projection based algorithm which…