Related papers: Neural Stochastic Dual Dynamic Programming
When looking for a solution, deterministic methods have the enormous advantage that they do find global optima. Unfortunately, they are very CPU-intensive, and are useless on untractable NP-hard problems that would require thousands of…
The increasing penetration of renewable energy requires greater use of storage resources to manage system intermittency. As a result, there is growing interest in evaluating the opportunity cost of stored energy, or usage values, which can…
Autonomous agents are limited in their ability to observe the world state. Partially observable Markov decision processes (POMDPs) formally model the problem of planning under world state uncertainty, but POMDPs with continuous actions and…
We propose a new algorithm for solving multistage stochastic mixed integer linear programming (MILP) problems with complete continuous recourse. In a similar way to cutting plane methods, we construct nonlinear Lipschitz cuts to build lower…
Connections between Deep Neural Networks (DNNs) training and optimal control theory has attracted considerable attention as a principled tool of algorithmic design. Differential Dynamic Programming (DDP) neural optimizer is a recently…
Trajectory following is one of the complicated control problems when its dynamics are nonlinear, stochastic and include a large number of parameters. The problem has significant difficulties including a large number of trials required for…
The most common approaches for solving multistage stochastic programming problems in the research literature have been to either use value functions ("dynamic programming") or scenario trees ("stochastic programming") to approximate the…
We present a novel linear program for the approximation of the dynamic programming cost-to-go function in high-dimensional stochastic control problems. LP approaches to approximate DP have typically relied on a natural `projection' of a…
A stagewise decomposition algorithm called value function gradient learning (VFGL) is proposed for large-scale multistage stochastic convex programs. VFGL finds the parameter values that best fit the gradient of the value function within a…
This work addresses an extended class of optimal control problems where a target for a system state has the form of an ellipsoid rather than a fixed, single point. As a computationally affordable method for resolving the extended problem,…
Recent focus on robustness to adversarial attacks for deep neural networks produced a large variety of algorithms for training robust models. Most of the effective algorithms involve solving the min-max optimization problem for training…
In this paper, we focus on a data-driven risk-averse multistage stochastic programming (RMSP) model considering distributional robustness. We optimize the RMSP over the worst-case distribution within an ambiguity set of probability…
Stochastic gradient descent (SGD) is a standard optimization method to minimize a training error with respect to network parameters in modern neural network learning. However, it typically suffers from proliferation of saddle points in the…
Stochastic gradient descent (SGD) with stochastic momentum is popular in nonconvex stochastic optimization and particularly for the training of deep neural networks. In standard SGD, parameters are updated by improving along the path of the…
Differential Dynamic Programming (DDP) is one of the indirect methods for solving an optimal control problem. Several extensions to DDP have been proposed to add stagewise state and control constraints, which can mainly be classified as…
This paper presents a novel deep learning framework for solving multiple optimal stopping problems in high dimensions. While deep learning has recently shown promise for single stopping problems, the multiple exercise case involves complex…
This paper presents a new theory, known as robust dynamic pro- gramming, for a class of continuous-time dynamical systems. Different from traditional dynamic programming (DP) methods, this new theory serves as a fundamental tool to analyze…
Stochastic Gradient Descent is used for large datasets to train models to reduce the training time. On top of that data parallelism is widely used as a method to efficiently train neural networks using multiple worker nodes in parallel.…
Moment-based distributionally robust optimization (DRO) provides an optimization framework to integrate statistical information with traditional optimization approaches. Under this framework, one assumes that the underlying joint…
Signal Temporal Logic (STL) has gained popularity in recent years as a specification language for cyber-physical systems, especially in robotics. Beyond being expressive and easy to understand, STL is appealing because the synthesis…