相关论文: A Gauss-Newton Method for Markov Decision Processe…

Newton method is one of the most powerful methods for finding solutions of nonlinear equations and for proving their existence. In its "pure" form it has fast convergence near the solution, but small convergence domain. On the other hand…

In this paper, a novel stochastic extra-step quasi-Newton method is developed to solve a class of nonsmooth nonconvex composite optimization problems. We assume that the gradient of the smooth part of the objective function can only be…

Optimization is important in machine learning problems, and quasi-Newton methods have a reputation as the most efficient numerical schemes for smooth unconstrained optimization. In this paper, we consider the explicit superlinear…

Optimization plays a key role in machine learning. Recently, stochastic second-order methods have attracted much attention due to their low computational cost in each iteration. However, these algorithms might perform poorly especially if…

Second-order Newton-type algorithms that leverage the exact Hessian or its approximation are central to solve nonlinear optimization problems. However, their applications in solving large-scale nonconvex problems are hindered by three…

We consider the problem of approximating the reachability probabilities in Markov decision processes (MDP) with uncountable (continuous) state and action spaces. While there are algorithms that, for special classes of such MDP, provide a…

We consider minimizing finite-sum and expectation objective functions via Hessian-averaging based subsampled Newton methods. These methods allow for gradient inexactness and have fixed per-iteration Hessian approximation costs. The recent…

Second-order methods for neural network optimization have several advantages over methods based on first-order gradient descent, including better scaling to large mini-batch sizes and fewer updates needed for convergence. But they are…

We present a novel statistical inference framework for convex empirical risk minimization, using approximate stochastic Newton steps. The proposed algorithm is based on the notion of finite differences and allows the approximation of a…

Advances in mobile computing technologies have made it possible to monitor and apply data-driven interventions across complex systems in real time. Markov decision processes (MDPs) are the primary model for sequential decision problems with…

Quasi-Newton methods employ an update rule that gradually improves the Hessian approximation using the already available gradient evaluations. We propose higher-order secant updates which generalize this idea to higher-order derivatives,…

Newton's method is a fundamental technique in optimization with quadratic convergence within a neighborhood around the optimum. However reaching this neighborhood is often slow and dominates the computational costs. We exploit two…

We propose and analyze a stochastic Newton algorithm for homogeneous distributed stochastic convex optimization, where each machine can calculate stochastic gradients of the same population objective, as well as stochastic Hessian-vector…

We propose policy gradient algorithms for robust infinite-horizon Markov decision processes (MDPs) with non-rectangular uncertainty sets, thereby addressing an open challenge in the robust MDP literature. Indeed, uncertainty sets that…

Calculating optimal policies is known to be computationally difficult for Markov decision processes (MDPs) with Borel state and action spaces. This paper studies finite-state approximations of discrete time Markov decision processes with…

We study the problem of computing deterministic optimal policies for constrained Markov decision processes (MDPs) with continuous state and action spaces, which are widely encountered in constrained dynamical systems. Designing…

Quasi-Newton algorithms are among the most popular iterative methods for solving unconstrained minimization problems, largely due to their favorable superlinear convergence property. However, existing results for these algorithms are…

Quasi-Newton (QN) methods provide an efficient alternative to second-order methods for minimizing smooth unconstrained problems. While QN methods generally compose a Hessian estimate based on one secant interpolation per iteration,…

Motivated by many application problems, we consider Markov decision processes (MDPs) with a general loss function and unknown parameters. To mitigate the epistemic uncertainty associated with unknown parameters, we take a Bayesian approach…

We present a novel Newton-type method for distributed optimization, which is particularly well suited for stochastic optimization and learning problems. For quadratic objectives, the method enjoys a linear rate of convergence which provably…