Benjamin J. Chasnov

Jason T. Isa, Bohan Wu, Qirui Wang et al.

As interactions between humans and AI become more prevalent, it is critical to have better predictors of human behavior in these interactions. We investigated how changes in the AI's adaptive algorithm impact behavior predictions in two-player continuous games. In our experiments, the AI adapted its actions using a gradient descent algorithm under different adaptation rates while human participants were provided cost feedback. The cost feedback was provided by one of two types of visual displays: (a) cost at the current joint action vector, or (b) cost in a local neighborhood of the current joint action vector. Our results demonstrate that AI adaptation rate can significantly affect human behavior, having the ability to shift the outcome between two game theoretic equilibrium. We observed that slow adaptation rates shift the outcome towards the Nash equilibrium, while fast rates shift the outcome towards the human-led Stackelberg equilibrium. The addition of localized cost information had the effect of shifting outcomes towards Nash, compared to the outcomes from cost information at only the current joint action vector. Future work will investigate other effects that influence the convergence of gradient descent games.

Benjamin J. Chasnov, Lillian J. Ratliff, Samuel A. Burden

Adaptive machines have the potential to assist or interfere with human behavior in a range of contexts, from cognitive decision-making to physical device assistance. Therefore it is critical to understand how machine learning algorithms can influence human actions, particularly in situations where machine goals are misaligned with those of people. Since humans continually adapt to their environment using a combination of explicit and implicit strategies, when the environment contains an adaptive machine, the human and machine play a game. Game theory is an established framework for modeling interactions between two or more decision-makers that has been applied extensively in economic markets and machine algorithms. However, existing approaches make assumptions about, rather than empirically test, how adaptation by individual humans is affected by interaction with an adaptive machine. Here we tested learning algorithms for machines playing general-sum games with human subjects. Our algorithms enable the machine to select the outcome of the co-adaptive interaction from a constellation of game-theoretic equilibria in action and policy spaces. Importantly, the machine learning algorithms work directly from observations of human actions without solving an inverse problem to estimate the human's utility function as in prior work. Surprisingly, one algorithm can steer the human-machine interaction to the machine's optimum, effectively controlling the human's actions even while the human responds optimally to their perceived cost landscape. Our results show that game theory can be used to predict and design outcomes of co-adaptive interactions between intelligent humans and machines.

Liyuan Zheng, Tanner Fiez, Zane Alumbaugh et al.

The hierarchical interaction between the actor and critic in actor-critic based reinforcement learning algorithms naturally lends itself to a game-theoretic interpretation. We adopt this viewpoint and model the actor and critic interaction as a two-player general-sum game with a leader-follower structure known as a Stackelberg game. Given this abstraction, we propose a meta-framework for Stackelberg actor-critic algorithms where the leader player follows the total derivative of its objective instead of the usual individual gradient. From a theoretical standpoint, we develop a policy gradient theorem for the refined update and provide a local convergence guarantee for the Stackelberg actor-critic algorithms to a local Stackelberg equilibrium. From an empirical standpoint, we demonstrate via simple examples that the learning dynamics we study mitigate cycling and accelerate convergence compared to the usual gradient dynamics given cost structures induced by actor-critic formulations. Finally, extensive experiments on OpenAI gym environments show that Stackelberg actor-critic algorithms always perform at least as well and often significantly outperform the standard actor-critic algorithm counterparts.

Tanner Fiez, Benjamin Chasnov, Lillian J. Ratliff

This paper investigates the convergence of learning dynamics in Stackelberg games. In the class of games we consider, there is a hierarchical game being played between a leader and a follower with continuous action spaces. We establish a number of connections between the Nash and Stackelberg equilibrium concepts and characterize conditions under which attracting critical points of simultaneous gradient descent are Stackelberg equilibria in zero-sum games. Moreover, we show that the only stable critical points of the Stackelberg gradient dynamics are Stackelberg equilibria in zero-sum games. Using this insight, we develop a gradient-based update for the leader while the follower employs a best response strategy for which each stable critical point is guaranteed to be a Stackelberg equilibrium in zero-sum games. As a result, the learning rule provably converges to a Stackelberg equilibria given an initialization in the region of attraction of a stable critical point. We then consider a follower employing a gradient-play update rule instead of a best response strategy and propose a two-timescale algorithm with similar asymptotic convergence guarantees. For this algorithm, we also provide finite-time high probability bounds for local convergence to a neighborhood of a stable Stackelberg equilibrium in general-sum games. Finally, we present extensive numerical results that validate our theory, provide insights into the optimization landscape of generative adversarial networks, and demonstrate that the learning dynamics we propose can effectively train generative adversarial networks.

Benjamin Chasnov, Lillian J. Ratliff, Eric Mazumdar et al.

Considering a class of gradient-based multi-agent learning algorithms in non-cooperative settings, we provide local convergence guarantees to a neighborhood of a stable local Nash equilibrium. In particular, we consider continuous games where agents learn in (i) deterministic settings with oracle access to their gradient and (ii) stochastic settings with an unbiased estimator of their gradient. Utilizing the minimum and maximum singular values of the game Jacobian, we provide finite-time convergence guarantees in the deterministic case. On the other hand, in the stochastic case, we provide concentration bounds guaranteeing that with high probability agents will converge to a neighborhood of a stable local Nash equilibrium in finite time. Different than other works in this vein, we also study the effects of non-uniform learning rates on the learning dynamics and convergence rates. We find that much like preconditioning in optimization, non-uniform learning rates cause a distortion in the vector field which can, in turn, change the rate of convergence and the shape of the region of attraction. The analysis is supported by numerical examples that illustrate different aspects of the theory. We conclude with discussion of the results and open questions.