Learning problems commonly exhibit an interesting feedback mechanism wherein the population data reacts to competing decision makers' actions. This paper formulates a new game theoretic framework for this phenomenon, called multi-player performative prediction. We focus on two distinct solution concepts, namely (i) performatively stable equilibria and (ii) Nash equilibria of the game. The latter equilibria are arguably more informative, but are generally computationally difficult to find since they are solutions of non-monotone games. We show that under mild assumptions, the performatively stable equilibria can be found efficiently by a variety of algorithms, including repeated retraining and the repeated (stochastic) gradient method. We then establish transparent sufficient conditions for strong monotonicity of the game and use them to develop algorithms for finding Nash equilibria. We investigate derivative free methods and adaptive gradient algorithms wherein each player alternates between learning a parametric description of their distribution and gradient steps on the empirical risk. Synthetic and semi-synthetic numerical experiments illustrate the results.

Learning problems commonly exhibit an interesting feedback mechanism wherein the population data reacts to competing decision makers’ actions. This paper formulates a new game theoretic framework for this phenomenon, called multi-player performative prediction. We establish transparent sufficient conditions for strong monotonicity of the game and use them to develop algorithms for finding Nash equilibria. We investigate derivative free methods and adaptive gradient algorithms wherein each player alternates between learning a parametric description of their distribution and gradient steps on the empirical risk. Synthetic and semi-synthetic numerical experiments illustrate the results.

We study gradient descent-ascent learning dynamics with timescale separation ($\tau$-GDA) in unconstrained continuous action zero-sum games where the minimizing player faces a nonconvex optimization problem and the maximizing player optimizes a Polyak-Lojasiewicz (PL) or strongly-concave (SC) objective. In contrast to past work on gradient-based learning in nonconvex-PL/SC zero-sum games, we assess convergence in relation to natural game-theoretic equilibria instead of only notions of stationarity. In pursuit of this goal, we prove that the only locally stable points of the $\tau$-GDA continuous-time limiting system correspond to strict local minmax equilibria in each class of games. For these classes of games, we exploit timescale separation to construct a potential function that when combined with the stability characterization and an asymptotic saddle avoidance result gives a global asymptotic almost-sure convergence guarantee for the discrete-time gradient descent-ascent update to a set of the strict local minmax equilibrium. Moreover, we provide convergence rates for the gradient descent-ascent dynamics with timescale separation to approximate stationary points.

In this article, we present an advanced coherent receiver for the IEEE 802.15.4 offset quadrature phase-shift keying (OQPSK) physical layer and provide an open-source implementation in the GNU Radio framework. Simulation and field test results show that the proposed receiver achieves about 11-dB power gain over an existing GNU Radio receiver, which treats OQPSK as minimum-shift-keying (MSK) for low-complexity processing. While suitable modules can be added to the MSK-based receiver for performance enhancement, the proposed receiver still maintains a 6-dB power gain. The proposed coherent receiver is attractive for IoT applications where a powerful software-defined-radio (SDR)-based gateway is deployed to interact with various sensors.