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We consider the unconstrained optimization problem whose objective function is composed of a smooth and a non-smooth conponents where the smooth component is the expectation a random function. This type of problem arises in some interesting…
We consider stochastic settings for clustering, and develop provably-good approximation algorithms for a number of these notions. These algorithms yield better approximation ratios compared to the usual deterministic clustering setting.…
We study stochastic convex optimization under infinite noise variance. Specifically, when the stochastic gradient is unbiased and has uniformly bounded $(1+\kappa)$-th moment, for some $\kappa \in (0,1]$, we quantify the convergence rate of…
Financial markets are complex environments that produce enormous amounts of noisy and non-stationary data. One fundamental problem is online portfolio selection, the goal of which is to exploit this data to sequentially select portfolios of…
We study a general problem of allocating limited resources to heterogeneous customers over time under model uncertainty. Each type of customer can be serviced using different actions, each of which stochastically consumes some combination…
We present the viewpoint that optimization problems encountered in machine learning can often be interpreted as minimizing a convex functional over a function space, but with a non-convex constraint set introduced by model parameterization.…
In this paper, we formulate an optimal ordering policy as a stochastic control problem where each firm decides the amount of input goods to order from their upstream suppliers based on the current inventory level of its output good. For…
A small investor provides liquidity at the best bid and ask prices of a limit order market. For small spreads and frequent orders of other market participants, we explicitly determine the investor's optimal policy and welfare. In doing so,…
We define a stochastic model of a two-sided limit order book in terms of its key quantities \textit{best bid [ask] price} and the \textit{standing buy [sell] volume density}. For a simple scaling of the discreteness parameters, that keeps…
We systematically develop a learning-based treatment of stochastic optimal control (SOC), relying on direct optimization of parametric control policies. We propose a derivation of adjoint sensitivity results for stochastic differential…
We consider the distributed optimization problem for a multi-agent system. Here, multiple agents cooperatively optimize an objective by sharing information through a communication network and performing computations. In this tutorial, we…
This paper investigates optimal portfolio strategies in a market where the drift is driven by an unobserved Markov chain. Information on the state of this chain is obtained from stock prices and expert opinions in the form of signals at…
Distributed stochastic optimization has drawn great attention recently due to its effectiveness in solving large-scale machine learning problems. Though numerous algorithms have been proposed and successfully applied to general practical…
Many real-world systems are characterized by stochastic dynamical rules where a complex network of interactions among individual elements probabilistically determines their state. Even with full knowledge of the network structure and of the…
This paper examines a variety of classical optimization problems, including well-known minimization tasks and more general variational inequalities. We consider a stochastic formulation of these problems, and unlike most previous work, we…
We study the optimal liquidation problem in a market model where the bid price follows a geometric pure jump process whose local characteristics are driven by an unobservable finite-state Markov chain and by the liquidation rate. This model…
This paper presents a stochastic, model predictive control (MPC) algorithm that leverages short-term probabilistic forecasts for dispatching and rebalancing Autonomous Mobility-on-Demand systems (AMoD, i.e. fleets of self-driving vehicles).…
Driven by the need to solve increasingly complex optimization problems in signal processing and machine learning, there has been increasing interest in understanding the behavior of gradient-descent algorithms in non-convex environments.…
In this paper, a distributed stochastic approximation algorithm is studied. Applications of such algorithms include decentralized estimation, optimization, control or computing. The algorithm consists in two steps: a local step, where each…
We consider stochastic optimization problems in multi-agent settings, where a network of agents aims to learn parameters which are optimal in terms of a global objective, while giving preference to locally observed streaming information. To…