Related papers: Global Optimization for Value Function Approximati…
In recent years, information relaxation and duality in dynamic programs have been studied extensively, and the resulted primal-dual approach has become a powerful procedure in solving dynamic programs by providing lower-upper bounds on the…
Market-based mechanisms such as auctions are being studied as an appropriate means for resource allocation in distributed and mulitagent decision problems. When agents value resources in combination rather than in isolation, they must often…
In this article we provide an experimental algorithm that in many cases gives us an upper bound of the global infimum of a real polynomial on $\R^{n}$. It is very well known that to find the global infimum of a real polynomial on $\R^{n}$,…
Low rank approximation is a commonly occurring problem in many computer vision and machine learning applications. There are two common ways of optimizing the resulting models. Either the set of matrices with a given rank can be explicitly…
We show that one can approximate the least fixed point solution for a multivariate system of monotone probabilistic max(min) polynomial equations, referred to as maxPPSs (and minPPSs, respectively), in time polynomial in both the encoding…
In this paper, we study the offline RL problem with linear function approximation. Our main structural assumption is that the MDP has low inherent Bellman error, which stipulates that linear value functions have linear Bellman backups with…
A fundamental problem in numerical analysis and approximation theory is approximating smooth functions by polynomials. A much harder version under recent consideration is to enforce bounds constraints on the approximating polynomial. In…
The problem of solving Markov decision processes under function approximation remains a fundamental challenge, even under linear function approximation settings. A key difficulty arises from a geometric mismatch: while the Bellman…
This article introduces an algorithm for implicit High Dimensional Model Representation (HDMR) of the Bellman equation. This approximation technique reduces memory demands of the algorithm considerably. Moreover, we show that HDMR enables…
We study the best approximation problem: \[ \displaystyle \min_{\alpha\in \mathbb R^m}\max_{1\leq i\leq n}\left|y_i -\sum_{j=1}^m \alpha_j \Gamma_j ({\bf x}_i) \right|. \] Here: $\Gamma:=\left\{\Gamma_1,...,\Gamma_m\right\}$ is a list of…
Gradient descent method, as one of the major methods in numerical optimization, is the key ingredient in many machine learning algorithms. As one of the most fundamental way to solve the optimization problems, it promises the function value…
Building on the blueprint from Goemans and Williamson (1995) for the Max-Cut problem, we construct a polynomial-time approximation algorithm for orthogonally constrained quadratic optimization problems. First, we derive a semidefinite…
In this paper, We propose a general Riemannian proximal optimization algorithm with guaranteed convergence to solve Markov decision process (MDP) problems. To model policy functions in MDP, we employ Gaussian mixture model (GMM) and…
Semidefinite programs are optimization methods with a wide array of applications, such as approximating difficult combinatorial problems. One such semidefinite program is the Goemans-Williamson algorithm, a popular integer relaxation…
While Bayesian neural networks (BNNs) have drawn increasing attention, their posterior inference remains challenging, due to the high-dimensional and over-parameterized nature. To address this issue, several highly flexible and scalable…
We consider a recently introduced fair repetitive scheduling problem involving a set of clients, each asking for their associated job to be daily scheduled on a single machine across a finite planning horizon. The goal is to determine a job…
In this paper, we describe a new method to compute the minimum of a real polynomial function and the ideal defining the points which minimize this polynomial function, assuming that the minimizer ideal is zero-dimensional. Our method is a…
This paper develops an inverse reinforcement learning algorithm aimed at recovering a reward function from the observed actions of an agent. We introduce a strategy to flexibly handle different types of actions with two approximations of…
Regularized Markov Decision Processes serve as models of sequential decision making under uncertainty wherein the decision maker has limited information processing capacity and/or aversion to model ambiguity. With functional approximation,…
It was recently shown in [http://arxiv.org/abs/1207.5518] that revenue optimization can be computationally efficiently reduced to welfare optimization in all multi-dimensional Bayesian auction problems with arbitrary (possibly…