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We introduce a new class of context dependent, incomplete information games to serve as structured prediction models for settings with significant strategic interactions. Our games map the input context to outcomes by first condensing the input into private player types that specify the utilities, weighted interactions, as well as the initial strategies for the players. The game is played over multiple rounds where players respond to weighted aggregates of their neighbors strategies. The predicted output from the model is a mixed strategy profile (a near-Nash equilibrium) and each observation is thought of as a sample from this strategy profile. We introduce two new aggregator paradigms with provably convergent game dynamics, and characterize the conditions under which our games are identifiable from data. Our games can be parameterized in a transferable manner so that the sets of players can change from one game to another. We demonstrate empirically that our games as models can recover meaningful strategic interactions from real voting data.
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This paper considers a networked aggregative game (NAG) where the players are distributed over a communication network. By only communicating with a subset of players, the goal of each player in the NAG is to minimize an individual cost function that depends on its own action and the aggregate of all the players actions. To this end, we design a novel distributed algorithm that jointly exploits the ideas of the consensus algorithm and the conditional projection descent. Under strongly monotone assumption on the pseudo-gradient mapping, the proposed algorithm with fixed step-sizes is proved to converge linearly to the unique Nash equilibrium of the NAG. Then the theoretical results are validated by numerical experiments.
We propose a fully asynchronous networked aggregative game (Asy-NAG) where each player minimizes a cost function that depends on its local action and the aggregate of all players actions. In sharp contrast to the existing NAGs, each player in our Asy-NAG can compute an estimate of the aggregate action at any wall-clock time by only using (possibly stale) information from nearby players of a directed network. Such an asynchronous update does not require any coordination among players. Moreover, we design a novel distributed algorithm with an aggressive mechanism for each player to adaptively adjust the optimization stepsize per update. Particularly, the slow players in terms of updating their estimates smartly increase their stepsizes to catch up with the fast ones. Then, we develop an augmented system approach to address the asynchronicity and the information delays between players, and rigorously show the convergence to a Nash equilibrium of the Asy-NAG via a perturbed coordinate algorithm which is also of independent interest. Finally, we evaluate the performance of the distributed algorithm through numerical simulations.
Human trajectory prediction is critical for autonomous platforms like self-driving cars or social robots. We present a latent belief energy-based model (LB-EBM) for diverse human trajectory forecast. LB-EBM is a probabilistic model with cost function defined in the latent space to account for the movement history and social context. The low-dimensionality of the latent space and the high expressivity of the EBM make it easy for the model to capture the multimodality of pedestrian trajectory distributions. LB-EBM is learned from expert demonstrations (i.e., human trajectories) projected into the latent space. Sampling from or optimizing the learned LB-EBM yields a belief vector which is used to make a path plan, which then in turn helps to predict a long-range trajectory. The effectiveness of LB-EBM and the two-step approach are supported by strong empirical results. Our model is able to make accurate, multi-modal, and social compliant trajectory predictions and improves over prior state-of-the-arts performance on the Stanford Drone trajectory prediction benchmark by 10.9% and on the ETH-UCY benchmark by 27.6%.
The study of strategic or adversarial manipulation of testing data to fool a classifier has attracted much recent attention. Most previous works have focused on two extreme situations where any testing data point either is completely adversarial or always equally prefers the positive label. In this paper, we generalize both of these through a unified framework for strategic classification, and introduce the notion of strategic VC-dimension (SVC) to capture the PAC-learnability in our general strategic setup. SVC provably generalizes the recent concept of adversarial VC-dimension (AVC) introduced by Cullina et al. arXiv:1806.01471. We instantiate our framework for the fundamental strategic linear classification problem. We fully characterize: (1) the statistical learnability of linear classifiers by pinning down its SVC; (2) its computational tractability by pinning down the complexity of the empirical risk minimization problem. Interestingly, the SVC of linear classifiers is always upper bounded by its standard VC-dimension. This characterization also strictly generalizes the AVC bound for linear classifiers in arXiv:1806.01471.
Consequential decision-making typically incentivizes individuals to behave strategically, tailoring their behavior to the specifics of the decision rule. A long line of work has therefore sought to counteract strategic behavior by designing more conservative decision boundaries in an effort to increase robustness to the effects of strategic covariate shift. We show that these efforts benefit the institutional decision maker at the expense of the individuals being classified. Introducing a notion of social burden, we prove that any increase in institutional utility necessarily leads to a corresponding increase in social burden. Moreover, we show that the negative externalities of strategic classification can disproportionately harm disadvantaged groups in the population. Our results highlight that strategy-robustness must be weighed against considerations of social welfare and fairness.
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