Related papers: Duality and DeepMartingale for High-Dimensional Op…

In the contextual linear bandit setting, algorithms built on the optimism principle fail to exploit the structure of the problem and have been shown to be asymptotically suboptimal. In this paper, we follow recent approaches of deriving…

In continuous-time portfolio selection for non-concave utility functions, the martingale duality approach is widely adopted in complete markets, while the dynamic programming approach may sometimes lead to singular solutions of the…

Finding tight bounds on the optimal solution is a critical element of practical solution methods for discrete optimization problems. In the last decade, decision diagrams (DDs) have brought a new perspective on obtaining upper and lower…

We introduce scalable algorithms for online learning of neural network parameters and Bayesian sequential decision making. Unlike classical Bayesian neural networks, which induce predictive uncertainty through a posterior over model…

We study martingale inequalities from an analytic point of view and show that a general martingale inequality can be reduced to a pair of deterministic inequalities in a small number of variables. More precisely, the optimal bound in the…

We analyse the convergence of the proximal gradient algorithm for convex composite problems in the presence of gradient and proximal computational inaccuracies. We derive new tighter deterministic and probabilistic bounds that we use to…

With the unprecedented growth of signal processing and machine learning application domains, there has been a tremendous expansion of interest in distributed optimization methods to cope with the underlying large-scale problems.…

This paper presents the Lagrangian duality theory for mixed-integer semidefinite programming (MISDP). We derive the Lagrangian dual problem and prove that the resulting Lagrangian dual bound dominates the bound obtained from the continuous…

In this paper, we address the contextual dueling bandit problem by proposing variance-aware algorithms that leverage neural networks to approximate nonlinear utility functions. Our approach employs a \textit{variance-aware exploration…

Information relaxation and duality in Markov decision processes have been studied recently by several researchers with the goal to derive dual bounds on the value function. In this paper we extend this dual formulation to controlled Markov…

Recent work in unsupervised representation learning has focused on learning deep directed latent-variable models. Fitting these models by maximizing the marginal likelihood or evidence is typically intractable, thus a common approximation…

In this work, we focus on variational Bayesian inference on the sparse Deep Neural Network (DNN) modeled under a class of spike-and-slab priors. Given a pre-specified sparse DNN structure, the corresponding variational posterior contraction…

In recent years, differential privacy has emerged as the de facto standard for sharing statistics of datasets while limiting the disclosure of private information about the involved individuals. This is achieved by randomly perturbing the…

We introduce the Pontryagin-Guided Direct Policy Optimization (PG-DPO) framework for high-dimensional continuous-time portfolio choice. Our approach combines Pontryagin's Maximum Principle (PMP) with backpropagation through time (BPTT) to…

When analyzing probabilistic computations, a powerful approach is to first find a martingale---an expression on the program variables whose expectation remains invariant---and then apply the optional stopping theorem in order to infer…

This paper develops algorithms for high-dimensional stochastic control problems based on deep learning and dynamic programming. Unlike classical approximate dynamic programming approaches, we first approximate the optimal policy by means of…

We study infinite-horizon Discounted Markov Decision Processes (DMDPs) under a generative model. Motivated by the Algorithm with Advice framework Mitzenmacher and Vassilvitskii 2022, we propose a novel framework to investigate how a…

We consider a Markov chain approximation scheme for utility maximization problems in continuous time, which uses, in turn, a piecewise constant policy approximation, Euler-Maruyama time stepping, and a Gauss-Hermite approximation of the…

The machine learning literature contains several constructions for prediction intervals that are intuitively reasonable but ultimately ad-hoc in that they do not come with provable performance guarantees. We present methods from the…

We study the compute-optimal trade-off between model and training data set sizes for large neural networks. Our result suggests a linear relation similar to that supported by the empirical analysis of chinchilla. While that work studies…