Related papers: Net gains in evolutionary dynamics: A unifying and…
We present a data-driven framework based on Lyapunov theory to provide stability guarantees for a family of hybrid systems. In particular, we are interested in the asymptotic stability of switching linear systems whose switching sequence is…
The computational capabilities of a neural network are widely assumed to be determined by its static architecture. Here we challenge this view by establishing that a fixed neural structure can operate in fundamentally different…
Designing a stabilizing controller for nonlinear systems is a challenging task, especially for high-dimensional problems with unknown dynamics. Traditional reinforcement learning algorithms applied to stabilization tasks tend to drive the…
Populations of replicating entities frequently experience sudden or cyclical changes in environment. We explore the implications of this phenomenon via a environmental switching parameter in several common evolutionary dynamics models…
We formulate and study a general time-varying multi-agent system where players repeatedly compete under incomplete information. Our work is motivated by scenarios commonly observed in online advertising and retail marketplaces, where agents…
We study the dynamics of individual agents in some kinetic models of wealth exchange, particularly, the models with savings. For the model with uniform savings, agents perform simple random walks in the "wealth space". On the other hand, we…
Stability analysis and control of linear impulsive systems is addressed in a hybrid framework, through the use of continuous-time time-varying discontinuous Lyapunov functions. Necessary and sufficient conditions for stability of impulsive…
We propose a stability analysis method for sampled-data switched linear systems with finite-level static quantizers. In the closed-loop system, information on the active mode of the plant is transmitted to the controller only at each…
The use of algorithmic predictions in decision-making leads to a feedback loop where the models we deploy actively influence the data distributions we see, and later use to retrain on. This dynamic was formalized by Perdomo et al. 2020 in…
We study population dynamics under which each revising agent tests each strategy k times, with each trial being against a newly drawn opponent, and chooses the strategy whose mean payoff was highest. When k = 1, defection is globally stable…
We study the problem of resilient strategies in the presence of uncertainty. Resilient strategies enable an agent to make decisions that are robust against disturbances. In particular, we are interested in those disturbances that are able…
We provide a framework to study stability notions for two-sided dynamic matching markets in which matching is one-to-one and irreversible. The framework gives center stage to the set of matchings an agent anticipates would ensue should they…
This paper develops a novel methodology to study robust stability properties of Nash equilibrium points in dynamic games. Small-gain techniques in modern mathematical control theory are used for the first time to derive conditions…
We study two-dimensional triangular-network models, which have degenerate ground states composed of straight or randomly-zigzagging stripes and thus sub-extensive residual entropy. We show that attraction is responsible for the inversion of…
Existing AI alignment approaches assume that preferences are static, which is unrealistic: our preferences change, and may even be influenced by our interactions with AI systems themselves. To clarify the consequences of incorrectly…
In this paper, we propose a dynamical systems perspective of the Expectation-Maximization (EM) algorithm. More precisely, we can analyze the EM algorithm as a nonlinear state-space dynamical system. The EM algorithm is widely adopted for…
In a stable matching problem there are two groups of agents, with agents on one side having their individual preferences for agents on another side as a potential match. It is assumed silently that agents can freely and costlessly ``switch"…
We propose two solution concepts for matchings under preferences: robustness and near stability. The former strengthens while the latter relaxes the classic definition of stability by Gale and Shapley (1962). Informally speaking, robustness…
What does it mean to fully understand the behavior of a network of adaptive agents? The golden standard typically is the behavior of learning dynamics in potential games, where many evolutionary dynamics, e.g., replicator, are known to…
We introduce the framework of performative reinforcement learning where the policy chosen by the learner affects the underlying reward and transition dynamics of the environment. Following the recent literature on performative…