Related papers: Mirror Descent Algorithms for Risk Budgeting Portf…
This paper is concerned with multi-agent optimization problem. A distributed randomized gradient-free mirror descent (DRGFMD) method is developed by introducing a randomized gradient-free oracle in the mirror descent scheme where the…
Stochastic multi-objective optimization (SMOO) has recently emerged as a powerful framework for addressing machine learning problems with multiple objectives. The bias introduced by the nonlinearity of the subproblem solution mapping…
Systemic risk measures were introduced to capture the global risk and the corresponding contagion effects that is generated by an interconnected system of financial institutions. To this purpose, two approaches were suggested. In the first…
We consider centralized and distributed mirror descent algorithms over a finite-dimensional Hilbert space, and prove that the problem variables converge to an optimizer of a possibly nonsmooth function when the step sizes are square…
Mirror Descent is a popular algorithm, that extends Gradients Descent (GD) beyond the Euclidean geometry. One of its benefits is to enable strong convergence guarantees through smooth-like analyses, even for objectives with exploding or…
First-order optimization methods tend to inherently favor certain solutions over others when minimizing an underdetermined training objective that has multiple global optima. This phenomenon, known as implicit bias, plays a critical role in…
We develop a generic policy gradient method with the global optimality guarantee for robust Markov Decision Processes (MDPs). While policy gradient methods are widely used for solving dynamic decision problems due to their scalable and…
While there is an extensive body of research analyzing policy gradient methods for discounted cumulative-reward MDPs, prior work on policy gradient methods for average-reward MDPs has been limited, with most existing results restricted to…
In portfolio analysis, the traditional approach of replacing population moments with sample counterparts may lead to suboptimal portfolio choices. I show that optimal portfolio weights can be estimated using a machine learning (ML)…
In this paper, we analyze the mirror descent algorithm for non-smooth optimization problems in which the objective function is relatively strongly convex, without relying on the standard Lipschitz continuity assumption commonly used in the…
Based on the ideas of arXiv:1710.06612, we consider the problem of minimization of the Holder-continuous non-smooth functional $f$ with non-positive convex (generally, non-smooth) Lipschitz-continuous functional constraint. We propose some…
We study discrete-time mirror descent applied to the unregularized empirical risk in matrix sensing. In both the general case of rectangular matrices and the particular case of positive semidefinite matrices, a simple potential-based…
Improving sample efficiency has been a longstanding goal in reinforcement learning. This paper proposes $\mathtt{VRMPO}$ algorithm: a sample efficient policy gradient method with stochastic mirror descent. In $\mathtt{VRMPO}$, a novel…
Mean-reverting behavior of individuals assets is widely known in financial markets. In fact, we can construct a portfolio that has mean-reverting behavior and use it in trading strategies to extract profits. In this paper, we show that we…
We consider the problem of optimizing a portfolio of financial assets, where the number of assets can be much larger than the number of observations. The optimal portfolio weights require estimating the inverse covariance matrix of excess…
In this paper, we analyze the local convergence rate of optimistic mirror descent methods in stochastic variational inequalities, a class of optimization problems with important applications to learning theory and machine learning. Our…
Recently there has been renewed interests in derivative free approaches to stochastic optimization. In this paper, we examine the rates of convergence for the Kiefer-Wolfowitz algorithm and the mirror descent algorithm, under various…
We introduce and analyze a new family of first-order optimization algorithms which generalizes and unifies both mirror descent and dual averaging. Within the framework of this family, we define new algorithms for constrained optimization…
We consider the problem of minimizing the sum of an average function of a large number of smooth convex components and a general, possibly non-differentiable, convex function. Although many methods have been proposed to solve this problem…
This paper introduces the $(\alpha, \Gamma)$-descent, an iterative algorithm which operates on measures and performs $\alpha$-divergence minimisation in a Bayesian framework. This gradient-based procedure extends the commonly-used…