Multi-agent systems exhibit complex behaviors that emanate from the interactions of multiple agents in a shared environment. In this work, we are interested in controlling one agent in a multi-agent system and successfully learn to interact with the other agents that have fixed policies. Modeling the behavior of other agents (opponents) is essential in understanding the interactions of the agents in the system. By taking advantage of recent advances in unsupervised learning, we propose modeling opponents using variational autoencoders. Additionally, many existing methods in the literature assume that the opponent models have access to opponent's observations and actions during both training and execution. To eliminate this assumption, we propose a modification that attempts to identify the underlying opponent model using only local information of our agent, such as its observations, actions, and rewards. The experiments indicate that our opponent modeling methods achieve equal or greater episodic returns in reinforcement learning tasks against another modeling method.

In two-player zero-sum games a Nash equilibrium strategy is guaranteed to win (or tie) in expectation against any opposing strategy by the minimax theorem. In games with m ore than two players there can be multiple equilibria with different values to the players, and follow ing one has no performance guarantee; however, it was shown that a Nash equilibrium strategy defeated a variet y of agents submitted for a class project in a 3-player imperfect-information game, Kuhn poker [13]. Thi s demonstrates that Nash equilibrium strategies can be successful in practice despite the fact that they do no t have a performance guarantee. While Nash equilibrium can be computed in polynomial time fo r two-player zero-sum games, it is PPAD-hard to compute for nonzero-sum and games with 3 or mor e agents and widely believed that no efficient algorithms exist [8, 9]. Counterfactual regret mi nimization (CFR) is an iterative self-play procedure that has been proven to converge to Nash equilibrium in two-p layer zero-sum [28].

We consider the problem of off-policy evaluation for reinforcement learning, where the goal is to estimate the expected reward of a target policy $\pi$ using offline data collected by running a logging policy $\mu$. Standard importance-sampling based approaches for this problem suffer from a variance that scales exponentially with time horizon $H$, which motivates a splurge of recent interest in alternatives that break the "Curse of Horizon" (Liu et al. 2018, Xie et al. 2019). In particular, it was shown that a marginalized importance sampling (MIS) approach can be used to achieve an estimation error of order $O(H^3/ n)$ in mean square error (MSE) under an episodic Markov Decision Process model with finite states and potentially infinite actions. The MSE bound however is still a factor of $H$ away from a Cramer-Rao lower bound of order $\Omega(H^2/n)$. In this paper, we prove that with a simple modification to the MIS estimator, we can asymptotically attain the Cramer-Rao lower bound, provided that the action space is finite. We also provide a general method for constructing MIS estimators with high-probability error bounds.

Navigating a new indoor space without any prior knowledge or even a map is a challenging task for a human, let alone a robot. To help develop intelligent machines that interact more effectively with complex 3D environments, Facebook researchers developed a GPU-accelerated deep reinforcement learning model that achieves near 100 percent success in navigating a variety of virtual environments without a pre-provided map. To achieve this breakthrough, the team focused their work on developing an efficient approach to scaling RL models, which require a significant number of training samples, using multi-node distribution. "A single parameter server and thousands of (typically CPU) workers may be fundamentally incompatible with the needs of modern computer vision and robotics communities," the researchers explained in their post, Near-perfect point-goal navigation from 2.5 billion frames of experience. "Unlike Gym or Atari, 3D simulators require GPU acceleration…. The desired agents operate from high-dimensional inputs (pixels) and use deep networks, such as ResNet50, which strain the parameter server. Thus, existing distributed RL architectures do not scale and there is a need to develop a new distributed architecture."

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The Probabilistic Serial mechanism is well-known for its desirable fairness and efficiency properties. It is one of the most prominent protocols for the random assignment problem. However, Probabilistic Serial is not incentive-compatible, thereby these desirable properties only hold for the agents' declared preferences, rather than their genuine preferences. A substantial utility gain through strategic behaviors would trigger self-interested agents to manipulate the mechanism and would subvert the very foundation of adopting the mechanism in practice. In this paper, we characterize the extent to which an individual agent can increase its utility by strategic manipulation. We show that the incentive ratio of the mechanism is $\frac{3}{2}$. That is, no agent can misreport its preferences such that its utility becomes more than 1.5 times of what it is when reports truthfully. This ratio is a worst-case guarantee by allowing an agent to have complete information about other agents' reports and to figure out the best response strategy even if it is computationally intractable in general. To complement this worst-case study, we further evaluate an agent's utility gain on average by experiments. The experiments show that an agent' incentive in manipulating the rule is very limited. These results shed some light on the robustness of Probabilistic Serial against strategic manipulation, which is one step further than knowing that it is not incentive-compatible.

Making sophisticated, robust, and safe sequential decisions is at the heart of intelligent systems. This is especially critical for planning in complex multi-agent environments, where agents need to anticipate other agents' intentions and possible future actions. Traditional methods formulate the problem as a Markov Decision Process, but the solutions often rely on various assumptions and become brittle when presented with corner cases. In contrast, deep reinforcement learning (Deep RL) has been very effective at finding policies by simultaneously exploring, interacting, and learning from environments. Leveraging the powerful Deep RL paradigm, we demonstrate that an iterative procedure of self-play can create progressively more diverse environments, leading to the learning of sophisticated and robust multi-agent policies. W e demonstrate this in a challenging multi-agent simulation of merging traffic, where agents must interact and negotiate with others in order to successfully merge on or off the road. While the environment starts off simple, we increase its complexity by iteratively adding an increasingly diverse set of agents to the agent "zoo" as training progresses. Qualitatively, we find that through self-play, our policies automatically learn interesting behaviors such as defensive driving, overtaking, yielding, and the use of signal lights to communicate intentions to other agents. In addition, quantitatively, we show a dramatic improvement of the success rate of merging maneuvers from 63% to over 98%.

Regret analysis is challenging in Multi-Agent Reinforcement Learning (MARL) primarily due to the dynamical environments and the decentralized information among agents. We attempt to solve this challenge in the context of decentralized learning in multi-agent linear-quadratic (LQ) dynamical systems. We begin with a simple setup consisting of two agents and two dynamically decoupled stochastic linear systems, each system controlled by an agent. The systems are coupled through a quadratic cost function. When both systems' dynamics are unknown and there is no communication among the agents, we show that no learning policy can generate sub-linear in $T$ regret, where $T$ is the time horizon. When only one system's dynamics are unknown and there is one-directional communication from the agent controlling the unknown system to the other agent, we propose a MARL algorithm based on the construction of an auxiliary single-agent LQ problem. The auxiliary single-agent problem in the proposed MARL algorithm serves as an implicit coordination mechanism among the two learning agents. This allows the agents to achieve a regret within $O(\sqrt{T})$ of the regret of the auxiliary single-agent problem. Consequently, using existing results for single-agent LQ regret, our algorithm provides a $\tilde{O}(\sqrt{T})$ regret bound. (Here $\tilde{O}(\cdot)$ hides constants and logarithmic factors). Our numerical experiments indicate that this bound is matched in practice. From the two-agent problem, we extend our results to multi-agent LQ systems with certain communication patterns.

This paper studies the decentralized optimization and learning problem where multiple interconnected agents aim to learn an optimal decision function defined over a reproducing kernel Hilbert (RKH) space by jointly minimizing a global objective function, with access to locally observed data only. As a non-parametric approach, kernel learning faces a major challenge in distributed implementation: the decision variables of local objective functions are data-dependent with different sizes and thus cannot be optimized under the decentralized consensus framework without any raw data exchange among agents. To circumvent this major challenge and preserve data privacy, we leverage the random feature (RF) approximation approach to map the large-volume data represented in the RKH space into a smaller RF space, which facilitates the same-size parameter exchange and enables distributed agents to reach consensus on the function decided by the parameters in the RF space. For fast convergent implementation, we design an iterative algorithm for Decentralized Kernel Learning via Alternating direction method of multipliers (DKLA). Further, we develop a COmmunication-censored KErnel learning (COKE) algorithm to reduce the communication load in DKLA. To do so, we apply a communication-censoring strategy, which prevents an agent from transmitting at every iteration unless its local updates are deemed informative. Theoretical results in terms of linear convergence guarantee and generalization performance analysis of DKLA and COKE are provided. Comprehensive tests with both synthetic and real datasets are conducted to verify the communication efficiency and learning effectiveness of COKE.

Reinforcement Learning (RL) has demonstrated a great potential for automatically solving decision making problems in complex uncertain environments. Basically, RL proposes a computational approach that allows learning through interaction in an environment of stochastic behavior, with agents taking actions to maximize some cumulative short-term and long-term rewards. Some of the most impressive results have been shown in Game Theory where agents exhibited super-human performance in games like Go or Starcraft 2, which led to its adoption in many other domains including Cloud Computing. Particularly, workflow autoscaling exploits the Cloud elasticity to optimize the execution of workflows according to a given optimization criteria. This is a decision-making problem in which it is necessary to establish when and how to scale-up/down computational resources; and how to assign them to the upcoming processing workload. Such actions have to be taken considering some optimization criteria in the Cloud, a dynamic and uncertain environment. Motivated by this, many works apply RL to the autoscaling problem in Cloud. In this work we survey exhaustively those proposals from major venues, and uniformly compare them based on a set of proposed taxonomies. We also discuss open problems and provide a prospective of future research in the area.