Abhinav Sinha

Deepanshu Vasal, Abhinav Sinha, Achilleas Anastasopoulos

We consider finite-horizon and infinite-horizon versions of a dynamic game with $N$ selfish players who observe their types privately and take actions that are publicly observed. Players' types evolve as conditionally independent Markov processes, conditioned on their current actions. Their actions and types jointly determine their instantaneous rewards. In dynamic games with asymmetric information, a widely used concept of equilibrium is perfect Bayesian equilibrium (PBE), which consists of a strategy and belief pair that simultaneously satisfy sequential rationality and belief consistency. In general, there does not exist a universal algorithm that decouples the interdependence of strategies and beliefs over time in calculating PBE. In this paper, for the finite-horizon game with independent types we develop a two-step backward-forward recursive algorithm that sequentially decomposes the problem (w.r.t. time) to obtain a subset of PBEs, which we refer to as structured Bayesian perfect equilibria (SPBE). In such equilibria, a player's strategy depends on its history only through a common public belief and its current private type. The backward recursive part of this algorithm defines an equilibrium generating function. Each period in the backward recursion involves solving a fixed-point equation on the space of probability simplexes for every possible belief on types. Using this function, equilibrium strategies and beliefs are generated through a forward recursion. We then extend this methodology to the infinite-horizon model, where we propose a time-invariant single-shot fixed-point equation, which in conjunction with a forward recursive step, generates the SPBE. Sufficient conditions for the existence of SPBE are provided. With our proposed method, we find equilibria that exhibit signaling behavior. This is illustrated with the help of a concrete public goods example.

Umer Siddique, Abhinav Sinha, Yongcan Cao

In this paper, we address the issue of fairness in preference-based reinforcement learning (PbRL) in the presence of multiple objectives. The main objective is to design control policies that can optimize multiple objectives while treating each objective fairly. Toward this objective, we design a new fairness-induced preference-based reinforcement learning or FPbRL. The main idea of FPbRL is to learn vector reward functions associated with multiple objectives via new welfare-based preferences rather than reward-based preference in PbRL, coupled with policy learning via maximizing a generalized Gini welfare function. Finally, we provide experiment studies on three different environments to show that the proposed FPbRL approach can achieve both efficiency and equity for learning effective and fair policies.

Umer Siddique, Abhinav Sinha, Yongcan Cao

In this paper, we propose an adaptive event-triggered reinforcement learning control for continuous-time nonlinear systems, subject to bounded uncertainties, characterized by complex interactions. Specifically, the proposed method is capable of jointly learning both the control policy and the communication policy, thereby reducing the number of parameters and computational overhead when learning them separately or only one of them. By augmenting the state space with accrued rewards that represent the performance over the entire trajectory, we show that accurate and efficient determination of triggering conditions is possible without the need for explicit learning triggering conditions, thereby leading to an adaptive non-stationary policy. Finally, we provide several numerical examples to demonstrate the effectiveness of the proposed approach.

Jacob Abernethy, Chansoo Lee, Abhinav Sinha et al.

We present a new optimization-theoretic approach to analyzing Follow-the-Leader style algorithms, particularly in the setting where perturbations are used as a tool for regularization. We show that adding a strongly convex penalty function to the decision rule and adding stochastic perturbations to data correspond to deterministic and stochastic smoothing operations, respectively. We establish an equivalence between "Follow the Regularized Leader" and "Follow the Perturbed Leader" up to the smoothness properties. This intuition leads to a new generic analysis framework that recovers and improves the previous known regret bounds of the class of algorithms commonly known as Follow the Perturbed Leader.