Related papers: On Convergence of Binary Trust-Region Steepest Des…
In this paper we study simulation based optimization algorithms for solving discrete time optimal stopping problems. This type of algorithms became popular among practioneers working in the area of quantitative finance. Using large…
Decentralized optimization is well studied for smooth unconstrained problems. However, constrained problems or problems with composite terms are an open direction for research. We study structured (or composite) optimization problems, where…
High-dimensional linear regression under heavy-tailed noise or outlier corruption is challenging, both computationally and statistically. Convex approaches have been proven statistically optimal but suffer from high computational costs,…
Gradient-based methods have been highly successful for solving a variety of both unconstrained and constrained nonlinear optimization problems. In real-world applications, such as optimal control or machine learning, the necessary function…
The trust region method is an algorithm traditionally used in the field of derivative free optimization. The method works by iteratively constructing surrogate models (often linear or quadratic functions) to approximate the true objective…
In this paper, we study a few challenging theoretical and numerical issues on the well known trust region policy optimization for deep reinforcement learning. The goal is to find a policy that maximizes the total expected reward when the…
This letter investigates the convergence and concentration properties of the Stochastic Mirror Descent (SMD) algorithm utilizing biased stochastic subgradients. We establish the almost sure convergence of the algorithm's iterates under the…
We consider mixed-integer optimal control problems with combinatorial constraints that couple over time such as minimum dwell times. We analyze a lifting and decomposition approach into a mixed-integer optimal control problem without…
In this paper, we study the convergence properties of a randomized block-coordinate descent algorithm for the minimization of a composite convex objective function, where the block-coordinates are updated asynchronously and randomly…
Learning systems are typically optimized by minimizing loss or maximizing reward, assuming that improvements in these signals reflect progress toward the true objective. However, when feedback reliability is unobservable, this assumption…
Bayesian doubly robust (DR) causal inference faces a fundamental dilemma: joint modeling of outcome and propensity score suffers from the feedback problem where outcome information contaminates propensity score estimation, while two-step…
In this paper, we provide the first provable linear-time (in the number of non-zero entries of the input) algorithm for approximately solving the generalized trust region subproblem (GTRS) of minimizing a quadratic function over a quadratic…
The iteration complexity of the block-coordinate descent (BCD) type algorithm has been under extensive investigation. It was recently shown that for convex problems the classical cyclic BCGD (block coordinate gradient descent) achieves an…
For a wireless multi-tier heterogeneous network with orthogonal spectrum allocation across tiers, we optimize the association probability and the fraction of spectrum allocated to each tier so as to maximize rate coverage. In practice, the…
In this paper, we develop an exact reformulation and a deterministic approximation for distributionally robust joint chance-constrained programmings (DRCCPs) with a general class of convex uncertain constraints under data-driven Wasserstein…
We investigate a difference-of-convex (DC) formulation where the second term is allowed to be weakly convex. We examine the precise behavior of a single iteration of the difference-of-convex algorithm (DCA), providing a tight…
In this paper, we analyze posterior consistency of a Bayesian data assimilation problem under discretization. We prove convergence rates for the discrete posterior to ground truth solution under both conforming discretization and finite…
Successive quadratic approximations, or second-order proximal methods, are useful for minimizing functions that are a sum of a smooth part and a convex, possibly nonsmooth part that promotes regularization. Most analyses of iteration…
In this paper, we develop and analyze sub-sampled trust-region methods for solving finite-sum optimization problems. These methods employ subsampling strategies to approximate the gradient and Hessian of the objective function,…
In this work, we introduce a novel stochastic second-order method, within the framework of a non-monotone trust-region approach, for solving the unconstrained, nonlinear, and non-convex optimization problems arising in the training of deep…