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A Mathematical Program with Equilibrium Constraints (MPEC) is formulated to capture the relationships between multiple Mobility Service Providers (MSPs) and the users of a multi-modal transport network. The network supply structure is defined through a novel supernetwork approach where users' daily trip chains are represented to model the mobility services used to reach each destination. At the upper level, a profit maximization formulation is introduced to describe each MSPs' behaviour. At the lower level, users within a class choose minimum cost routes, according to Wardrop's first equilibrium principle. To consider the interactions between modes, non-separable costs between supernetwork links are defined, and users' equilibrium conditions are formulated as a Variational Inequality (VI). To solve the MPEC, an iterative solution algorithm based on a Modified Projection Method is proposed. Numerical examples are presented to illustrate properties of the model, and to examine scenarios showcasing cooperation or competition strategies between MSPs.

Adversarial team games model multiplayer strategic interactions in which a team of identically-interested players is competing against an adversarial player in a zero-sum game. Such games capture many well-studied settings in game theory, such as congestion games, but go well-beyond to environments wherein the cooperation of one team -- in the absence of explicit communication -- is obstructed by competing entities; the latter setting remains poorly understood despite its numerous applications. Since the seminal work of Von Stengel and Koller (GEB `97), different solution concepts have received attention from an algorithmic standpoint. Yet, the complexity of the standard Nash equilibrium has remained open. In this paper, we settle this question by showing that computing a Nash equilibrium in adversarial team games belongs to the class continuous local search (CLS), thereby establishing CLS-completeness by virtue of the recent CLS-hardness result of Rubinstein and Babichenko (STOC `21) in potential games. To do so, we leverage linear programming duality to prove that any $\epsilon$-approximate stationary strategy for the team can be extended in polynomial time to an $O(\epsilon)$-approximate Nash equilibrium, where the $O(\cdot)$ notation suppresses polynomial factors in the description of the game. As a consequence, we show that the Moreau envelop of a suitable best response function acts as a potential under certain natural gradient-based dynamics.

Taxi-demand prediction is an important application of machine learning that enables taxi-providing facilities to optimize their operations and city planners to improve transportation infrastructure and services. However, the use of sensitive data in these systems raises concerns about privacy and security. In this paper, we propose the use of federated learning for taxi-demand prediction that allows multiple parties to train a machine learning model on their own data while keeping the data private and secure. This can enable organizations to build models on data they otherwise would not be able to access. Evaluation with real-world data collected from 16 taxi service providers in Japan over a period of six months showed that the proposed system can predict the demand level accurately within 1\% error compared to a single model trained with integrated data.

Conventional Gaussian process regression exclusively assumes the existence of noise in the output data of model observations. In many scientific and engineering applications, however, the input locations of observational data may also be compromised with uncertainties owing to modeling assumptions, measurement errors, etc. In this work, we propose a Bayesian method that integrates the variability of input data into Gaussian process regression. Considering two types of observables -- noise-corrupted outputs with fixed inputs and those with prior-distribution-defined uncertain inputs, a posterior distribution is estimated via a Bayesian framework to infer the uncertain data locations. Thereafter, such quantified uncertainties of inputs are incorporated into Gaussian process predictions by means of marginalization. The effectiveness of this new regression technique is demonstrated through several numerical examples, in which a consistently good performance of generalization is observed, while a substantial reduction in the predictive uncertainties is achieved by the Bayesian inference of uncertain inputs.

Among the great successes of Reinforcement Learning (RL), self-play algorithms play an essential role in solving competitive games. Current self-play algorithms optimize the agent to maximize expected win-rates against its current or historical copies, making it often stuck in the local optimum and its strategy style simple and homogeneous. A possible solution is to improve the diversity of policies, which helps the agent break the stalemate and enhances its robustness when facing different opponents. However, enhancing diversity in the self-play algorithms is not trivial. In this paper, we aim to introduce diversity from the perspective that agents could have diverse risk preferences in the face of uncertainty. Specifically, we design a novel reinforcement learning algorithm called Risk-sensitive Proximal Policy Optimization (RPPO), which smoothly interpolates between worst-case and best-case policy learning and allows for policy learning with desired risk preferences. Seamlessly integrating RPPO with population-based self-play, agents in the population optimize dynamic risk-sensitive objectives with experiences from playing against diverse opponents. Empirical results show that our method achieves comparable or superior performance in competitive games and that diverse modes of behaviors emerge. Our code is public online at \url{//github.com/Jackory/RPBT}.

Developing AI tools that preserve fairness is of critical importance, specifically in high-stakes applications such as those in healthcare. However, health AI models' overall prediction performance is often prioritized over the possible biases such models could have. In this study, we show one possible approach to mitigate bias concerns by having healthcare institutions collaborate through a federated learning paradigm (FL; which is a popular choice in healthcare settings). While FL methods with an emphasis on fairness have been previously proposed, their underlying model and local implementation techniques, as well as their possible applications to the healthcare domain remain widely underinvestigated. Therefore, we propose a comprehensive FL approach with adversarial debiasing and a fair aggregation method, suitable to various fairness metrics, in the healthcare domain where electronic health records are used. Not only our approach explicitly mitigates bias as part of the optimization process, but an FL-based paradigm would also implicitly help with addressing data imbalance and increasing the data size, offering a practical solution for healthcare applications. We empirically demonstrate our method's superior performance on multiple experiments simulating large-scale real-world scenarios and compare it to several baselines. Our method has achieved promising fairness performance with the lowest impact on overall discrimination performance (accuracy).

Game-theoretic interactions with AI agents could differ from traditional human-human interactions in various ways. One such difference is that it may be possible to simulate an AI agent (for example because its source code is known), which allows others to accurately predict the agent's actions. This could lower the bar for trust and cooperation. In this paper, we formalize games in which one player can simulate another at a cost. We first derive some basic properties of such games and then prove a number of results for them, including: (1) introducing simulation into generic-payoff normal-form games makes them easier to solve; (2) if the only obstacle to cooperation is a lack of trust in the possibly-simulated agent, simulation enables equilibria that improve the outcome for both agents; and however (3) there are settings where introducing simulation results in strictly worse outcomes for both players.

Game theory has by now found numerous applications in various fields, including economics, industry, jurisprudence, and artificial intelligence, where each player only cares about its own interest in a noncooperative or cooperative manner, but without obvious malice to other players. However, in many practical applications, such as poker, chess, evader pursuing, drug interdiction, coast guard, cyber-security, and national defense, players often have apparently adversarial stances, that is, selfish actions of each player inevitably or intentionally inflict loss or wreak havoc on other players. Along this line, this paper provides a systematic survey on three main game models widely employed in adversarial games, i.e., zero-sum normal-form and extensive-form games, Stackelberg (security) games, zero-sum differential games, from an array of perspectives, including basic knowledge of game models, (approximate) equilibrium concepts, problem classifications, research frontiers, (approximate) optimal strategy seeking techniques, prevailing algorithms, and practical applications. Finally, promising future research directions are also discussed for relevant adversarial games.

Deep learning is usually described as an experiment-driven field under continuous criticizes of lacking theoretical foundations. This problem has been partially fixed by a large volume of literature which has so far not been well organized. This paper reviews and organizes the recent advances in deep learning theory. The literature is categorized in six groups: (1) complexity and capacity-based approaches for analyzing the generalizability of deep learning; (2) stochastic differential equations and their dynamic systems for modelling stochastic gradient descent and its variants, which characterize the optimization and generalization of deep learning, partially inspired by Bayesian inference; (3) the geometrical structures of the loss landscape that drives the trajectories of the dynamic systems; (4) the roles of over-parameterization of deep neural networks from both positive and negative perspectives; (5) theoretical foundations of several special structures in network architectures; and (6) the increasingly intensive concerns in ethics and security and their relationships with generalizability.

Reinforcement learning is one of the core components in designing an artificial intelligent system emphasizing real-time response. Reinforcement learning influences the system to take actions within an arbitrary environment either having previous knowledge about the environment model or not. In this paper, we present a comprehensive study on Reinforcement Learning focusing on various dimensions including challenges, the recent development of different state-of-the-art techniques, and future directions. The fundamental objective of this paper is to provide a framework for the presentation of available methods of reinforcement learning that is informative enough and simple to follow for the new researchers and academics in this domain considering the latest concerns. First, we illustrated the core techniques of reinforcement learning in an easily understandable and comparable way. Finally, we analyzed and depicted the recent developments in reinforcement learning approaches. My analysis pointed out that most of the models focused on tuning policy values rather than tuning other things in a particular state of reasoning.