Related papers: Sample Complexity of Data-driven Multistage Stocha…
We present a scheme for sequential decision making with a risk-sensitive objective and constraints in a dynamic environment. A neural network is trained as an approximator of the mapping from parameter space to space of risk and policy with…
Based on the stochastic maximum principle for the partially coupled forward-backward stochastic control system (FBSCS for short), a modified method of successive approximations (MSA for short) is established for stochastic recursive optimal…
To model combinatorial decision problems involving uncertainty and probability, we introduce scenario based stochastic constraint programming. Stochastic constraint programs contain both decision variables, which we can set, and stochastic…
The problem of optimising functions with intractable gradients frequently arise in machine learning and statistics, ranging from maximum marginal likelihood estimation procedures to fine-tuning of generative models. Stochastic approximation…
Bilevel optimization problems are receiving increasing attention in machine learning as they provide a natural framework for hyperparameter optimization and meta-learning. A key step to tackle these problems is the efficient computation of…
We consider chance-constrained problems with discrete random distribution. We aim for problems with a large number of scenarios. We propose a novel method based on the stochastic gradient descent method which performs updates of the…
Sequential optimization methods are often confronted with the curse of dimensionality in high-dimensional spaces. Current approaches under the Gaussian process framework are still burdened by the computational complexity of tracking…
We study the problem of sequentially testing whether a given stochastic process is generated by a known Markov chain. Formally, given access to a stream of random variables, we want to quickly determine whether this sequence is a trajectory…
This paper presents a detailed theoretical analysis of the three stochastic approximation proximal gradient algorithms proposed in our companion paper [49] to set regularization parameters by marginal maximum likelihood estimation. We prove…
Sample average approximation (SAA) is a technique for obtaining approximate solutions to stochastic programs that uses the average from a random sample to approximate the expected value that is being optimized. Since the outcome from…
We investigate a simple approximation scheme, based on overlapping linear decision rules, for solving data-driven two-stage distributionally robust optimization problems with the type-$\infty$ Wasserstein ambiguity set. Our main result…
We introduce a novel and efficient algorithm called the stochastic approximate gradient descent (SAGD), as an alternative to the stochastic gradient descent for cases where unbiased stochastic gradients cannot be trivially obtained.…
We are interested in understanding stability (almost sure boundedness) of stochastic approximation algorithms (SAs) driven by a `controlled Markov' process. Analyzing this class of algorithms is important, since many reinforcement learning…
We present Fast Approximate Minimum Spanning Tree (FAMST), a novel algorithm that addresses the computational challenges of constructing Minimum Spanning Trees (MSTs) for large-scale and high-dimensional datasets. FAMST utilizes a…
We consider stochastic optimization problems with non-convex functional constraints, such as those arising in trajectory generation, sparse approximation, and robust classification. To this end, we put forth a recursive momentum-based…
In this paper, we consider a class of stochastic optimal control problems with risk constraints that are expressed as bounded probabilities of failure for particular initial states. We present here a martingale approach that diffuses a risk…
The curse of dimensionality is a widely known issue in reinforcement learning (RL). In the tabular setting where the state space $\mathcal{S}$ and the action space $\mathcal{A}$ are both finite, to obtain a nearly optimal policy with…
We consider Markov decision processes (MDPs) in which the transition probabilities and rewards belong to an uncertainty set parametrized by a collection of random variables. The probability distributions for these random parameters are…
Stochastic approximation (SA) is an iterative algorithm for finding the fixed point of an operator using noisy samples and widely used in optimization and Reinforcement Learning (RL). The noise in RL exhibits a Markovian structure, and in…
Performance-based engineering for natural hazards facilitates the design and appraisal of structures with rigorous evaluation of their uncertain structural behavior under potentially extreme stochastic loads expressed in terms of failure…