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We study a variant of a recently introduced min-max optimization framework where the max-player is constrained to update its parameters in a greedy manner until it reaches a first-order stationary point. Our equilibrium definition for this…
We study problems arising in real-time auction markets, common in e-commerce and computational advertising, where bidders face the problem of calculating optimal bids. We focus upon a contract management problem where a demand aggregator is…
We propose a game-theoretic framework that incorporates both incomplete information and general ambiguity attitudes on factors external to all players. Our starting point is players' preferences on payoff-distribution vectors, essentially…
Recent successes of game-theoretic formulations in ML have caused a resurgence of research interest in differentiable games. Overwhelmingly, that research focuses on methods and upper bounds on their speed of convergence. In this work, we…
Evolutionary strategies have recently been shown to achieve competing levels of performance for complex optimization problems in reinforcement learning. In such problems, one often needs to optimize an objective function subject to a set of…
Optimal mechanisms have been provided in quite general multi-item settings, as long as each bidder's type distribution is given explicitly by listing every type in the support along with its associated probability. In the implicit setting,…
Securities markets are quintessential complex adaptive systems in which heterogeneous agents compete in an attempt to maximize returns. Species of trading agents are also subject to evolutionary pressure as entire classes of strategies…
In this paper we deal with stochastic optimization problems where the data distributions change in response to the decision variables. Traditionally, the study of optimization problems with decision-dependent distributions has assumed…
In recent years, constrained optimization has become increasingly relevant to the machine learning community, with applications including Neyman-Pearson classification, robust optimization, and fair machine learning. A natural approach to…
Previous work on the competitive retrieval setting focused on a single-query setting: document authors manipulate their documents so as to improve their future ranking for a given query. We study a competitive setting where authors opt to…
In multi-agent reinforcement learning (MARL) and game theory, agents repeatedly interact and revise their strategies as new data arrives, producing a sequence of strategy profiles. This paper studies sequences of strategies satisfying a…
This paper studies online optimization under inventory (budget) constraints. While online optimization is a well-studied topic, versions with inventory constraints have proven difficult. We consider a formulation of inventory-constrained…
In this paper I present several algorithmic techniques for improving the decision process of multiple types of agents behaving in environments where their interests are in conflict. The interactions between the agents are modelled by using…
This material provides thorough tutorials on some optimization techniques frequently used in various engineering disciplines, including convex optimization, linearization techniques and mixed-integer linear programming, robust optimization,…
This work focuses on the mathematical study of constant function market makers. We rigorously establish the conditions for optimal trading under the assumption of a quasilinear, but not necessarily convex (or concave), trade function. This…
The connection between game theory, convex optimization, and geometry is deep. There are many applications of linear programming methods and polyhedral representation conversion methods in game theory. In this paper, we discuss two more…
The topics treated in this thesis are inherently two-fold. The first part considers the problem of a market maker optimally setting bid/ask quotes over a finite time horizon, to maximize her expected utility. The intensities of the orders…
Can deep reinforcement learning algorithms be exploited as solvers for optimal trading strategies? The aim of this work is to test reinforcement learning algorithms on conceptually simple, but mathematically non-trivial, trading…
We consider a broker who has to place a large order which consumes a sizable part of average daily trading volume. The broker's aim is thus to minimize execution costs he incurs from the adverse impact of his trades on market prices. By…
We consider some classical optimization problems in path planning and network transport, and we introduce new auction-based algorithms for their optimal and suboptimal solution. The algorithms are based on mathematical ideas that are…