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Despite its popularity in the reinforcement learning community, a provably convergent policy gradient method for continuous space-time control problems with nonlinear state dynamics has been elusive. This paper proposes proximal gradient…
Dynamic game theory is an increasingly popular tool for modeling multi-agent, e.g. human-robot, interactions. Game-theoretic models presume that each agent wishes to minimize a private cost function that depends on others' actions. These…
We introduce a formalism modelling communication of distributed agents strictly in continuous-time. Within this framework, we study the problem of synthesising local strategies for individual agents such that a specified set of goal states…
This paper investigates the fixed-time consensus problem for a class of multi-agent systems with simple dynamics. Unlike the traditional way to realize fixed-time convergence, a novel strategy using the property of periodic functions is…
We study a time-inconsistent singular control problem originating from irreversible reinsurance decisions with non-exponential discount. A novel definition of equilibrium for time-inconsistent singular control problems is introduced. For…
Modeling the purposeful behavior of imperfect agents from a small number of observations is a challenging task. When restricted to the single-agent decision-theoretic setting, inverse optimal control techniques assume that observed behavior…
We study existence and uniqueness of the fixed points solutions of a large class of non-linear variable discounted transfer operators associated to a sequential decision-making process. We establish regularity properties of these solutions,…
Through a stochastic control theoretic approach, we analyze reputation games where a strategic long-lived player acts in a sequential repeated game against a collection of short-lived players. The key assumption in our model is that the…
Many decision problems in economics, information technology, and industry can be transformed to an optimal stopping of adapted random vectors with some utility function over the set of Markov times with respect to filtration build by the…
We propose a model in which dividend payments occur at regular, deterministic intervals in an otherwise continuous model. This contrasts traditional models where either the payment of continuous dividends is controlled or the dynamics are…
Recent results in the literature have provided connections between the so-called turnpike property, near optimality of closed-loop solutions, and strict dissipativity. Motivated by applications in economics, optimal control problems with…
We consider a general time-inconsistent stochastic linear-quadratic differential game. The time-inconsistency arises from the presence of quadratic terms of the expected state as well as state-dependent term in the objective functionals. We…
This paper studies a class of strongly monotone games involving non-cooperative agents that optimize their own time-varying cost functions. We assume that the agents can observe other agents' historical actions and choose actions that best…
Nonzero-sum stochastic differential games with impulse controls offer a realistic and far-reaching modelling framework for applications within finance, energy markets, and other areas, but the difficulty in solving such problems has…
We study deterministic, discrete linear time-invariant systems with infinite-horizon discounted quadratic cost. It is well-known that standard stabilizability and detectability properties are not enough in general to conclude stability…
Policy iteration is one of the classical frameworks of reinforcement learning, which requires a known initial stabilizing control. However, finding the initial stabilizing control depends on the known system model. To relax this requirement…
This paper examines the impact of agents' myopic optimization on the efficiency of systems comprised by many selfish agents. In contrast to standard congestion games where agents interact in a one-shot fashion, in our model each agent…
Time inconsistency is prevalent in dynamic choice problems: a plan of actions to be taken in the future that is optimal for an agent today may not be optimal for the same agent in the future. If the agent is aware of this intra-personal…
We study learning dynamics induced by strategic agents who repeatedly play a game with an unknown payoff-relevant parameter. In each step, an information system estimates a belief distribution of the parameter based on the players'…
Stochastic games with discounted payoff, introduced by Shapley, model adversarial interactions in stochastic environments where two players try to optimize a discounted sum of rewards. In this model, long-term weights are geometrically…