We address cost identification in a finite-horizon linear quadratic Gaussian game. We characterize the set of cost parameters that generate a given Nash equilibrium policy. We propose a backpropagation algorithm to identify the time-varying cost parameters. We derive a probabilistic error bound when the cost parameters are identified from finite trajectories. We test our method in numerical and driving simulations. Our algorithm identifies the cost parameters that can reproduce the Nash equilibrium policy and trajectory observations.

Safety is critical during human-robot interaction. But -- because people are inherently unpredictable -- it is often difficult for robots to plan safe behaviors. Instead of relying on our ability to anticipate humans, here we identify robot policies that are robust to unexpected human decisions. We achieve this by formulating human-robot interaction as a zero-sum game, where (in the worst case) the human's actions directly conflict with the robot's objective. Solving for the Nash Equilibrium of this game provides robot policies that maximize safety and performance across a wide range of human actions. Existing approaches attempt to find these optimal policies by leveraging Hamilton-Jacobi analysis (which is intractable) or linear-quadratic approximations (which are inexact). By contrast, in this work we propose a computationally efficient and theoretically justified method that converges towards the Nash Equilibrium policy. Our approach (which we call MCLQ) leverages linear-quadratic games to obtain an initial guess at safe robot behavior, and then iteratively refines that guess with a Monte Carlo search. Not only does MCLQ provide real-time safety adjustments, but it also enables the designer to tune how conservative the robot is -- preventing the system from focusing on unrealistic human behaviors. Our simulations and user study suggest that this approach advances safety in terms of both computation time and expected performance. See videos of our experiments here: https://youtu.be/KJuHeiWVuWY.

T o address this problem, BSs can work collaboratively to deliver a smooth migration (or handoff) and satisfy the UEs' service requirements. This paper formulates the load balancing problem as a Markov game and proposes a Robust Multi-agent Attention Actor-Critic (Robust-MA3C) algorithm that can facilitate collaboration among the BSs (i.e., agents). In particular, to solve the Markov game and find a Nash equilibrium policy, we embrace the idea of adopting a nature agent to model the system uncertainty. Moreover, we utilize the self-attention mechanism, which encourages high-performance BSs to assist low-performance BSs. In addition, we consider two types of schemes, which can facilitate load balancing for both active UEs and idle UEs. We carry out extensive evaluations by simulations, and simulation results illustrate that, compared to the state-of-the-art MARL methods, Robust-MA3C scheme can improve the overall performance by up to 45%.

This paper considers the problem of inverse reinforcement learning in zero-sum stochastic games when expert demonstrations are known to be not optimal. Compared to previous works that decouple agents in the game by assuming optimality in expert strategies, we introduce a new objective function that directly pits experts against Nash Equilibrium strategies, and we design an algorithm to solve for the reward function in the context of inverse reinforcement learning with deep neural networks as model approximations. In our setting the model and algorithm do not decouple by agent. In order to find Nash Equilibrium in large-scale games, we also propose an adversarial training algorithm for zero-sum stochastic games, and show the theoretical appeal of non-existence of local optima in its objective function. In our numerical experiments, we demonstrate that our Nash Equilibrium and inverse reinforcement learning algorithms address games that are not amenable to previous approaches using tabular representations. Moreover, with sub-optimal expert demonstrations our algorithms recover both reward functions and strategies with good quality.

We extend the potential-based shaping method from Markov decision processes to multi-player general-sum stochastic games. We prove that the Nash equilibria in a stochastic game remains unchanged after potential-based shaping is applied to the environment. The property of policy invariance provides a possible way of speeding convergence when learning to play a stochastic game.