Extensive-form games are a common model for multiagent interactions with imperfect information. In two-player zero-sum games, the typical solution concept is a Nash equilibrium over the unconstrained strategy set for each player. In many situations, however, we would like to constrain the set of possible strategies. For example, constraints are a natural way to model limited resources, risk mitigation, safety, consistency with past observations of behavior, or other secondary objectives for an agent. In small games, optimal strategies under linear constraints can be found by solving a linear program; however, state-of-the-art algorithms for solving large games cannot handle general constraints. In this work we introduce a generalized form of Counterfactual Regret Minimization that provably finds optimal strategies under any feasible set of convex constraints. We demonstrate the effectiveness of our algorithm for finding strategies that mitigate risk in security games, and for opponent modeling in poker games when given only partial observations of private information.

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Starcraft II (SCII) is widely considered as the most challenging Real Time Strategy (RTS) game as of now, due to large observation space, huge (continuous and infinite) action space, partial observation, multi-player simultaneous game model, long time horizon decision, etc. To push the frontier of AI's capability, Deepmind and Blizzard jointly present the StarCraft II Learning Environment (SC2LE) --- a testbench for designing complex decision making systems. While SC2LE provides a few mini games such as \textit{MoveToBeacon}, \textit{CollectMineralShards}, and \textit{DefeatRoaches} where some AI agents achieve the professional player's level, it is still far away from achieving the professional level in a \emph{full} game. To initialize the research and investigation in the full game, we develop two AI agents --- the AI agent TStarBot1 is based on deep reinforcement learning over flat action structure, and the AI agent TStarBot2 is based on rule controller over hierarchical action structure. Both TStarBot1 and TStarBot2 are able to defeat the builtin AI agents from level 1 to level 10 in a full game (1v1 \textit{Zerg}-vs-\textit{Zerg} game on the AbyssalReef map), noting that level 8, level 9, and level 10 are cheating agents with full vision on the whole map, with resource harvest boosting, and with both, respectively \footnote{According to some informal discussions from the StarCraft II forum, level 10 builtin AI is estimated to be Platinum to Diamond~\cite{scii-forum}, which are equivalent to top 50\% - 30\% human players in the ranking system of Battle.net Leagues~\cite{liquid}. }.

We present an effective technique for training deep learning agents capable of negotiating on a set of clauses in a contract agreement using a simple communication protocol. We use Multi Agent Reinforcement Learning to train both agents simultaneously as they negotiate with each other in the training environment. We also model selfish and prosocial behavior to varying degrees in these agents. Empirical evidence is provided showing consistency in agent behaviors. We further train a meta agent with a mixture of behaviors by learning an ensemble of different models using reinforcement learning. Finally, to ascertain the deployability of the negotiating agents, we conducted experiments pitting the trained agents against human players. Results demonstrate that the agents are able to hold their own against human players, often emerging as winners in the negotiation. Our experiments demonstrate that the meta agent is able to reasonably emulate human behavior.

We propose graph-dependent implicit regularisation strategies for distributed stochastic subgradient descent (Distributed SGD) for convex problems in multi-agent learning. Under the standard assumptions of convexity, Lipschitz continuity, and smoothness, we establish statistical learning rates that retain, up to logarithmic terms, centralised statistical guarantees through implicit regularisation (step size tuning and early stopping) with appropriate dependence on the graph topology. Our approach avoids the need for explicit regularisation in decentralised learning problems, such as adding constraints to the empirical risk minimisation rule. Particularly for distributed methods, the use of implicit regularisation allows the algorithm to remain simple, without projections or dual methods. To prove our results, we establish graph-independent generalisation bounds for Distributed SGD that match the centralised setting (using algorithmic stability), and we establish graph-dependent optimisation bounds that are of independent interest. We present numerical experiments to show that the qualitative nature of the upper bounds we derive can be representative of real behaviours. Keywords: Distributed machine learning, implicit regularisation, generalisation bounds, algorithmic stability, multi-agent optimisation.

Although many reinforcement learning methods have been proposed for learning the optimal solutions in single-agent continuousaction domains, multiagent coordination domains with continuous actions have received relatively few investigations. In this paper, we propose an independent learner hierarchical method, named Sample Continuous Coordination with recursive Frequency Maximum Q-Value (SCC-rFMQ), which divides the cooperative problem with continuous actions into two layers. The first layer samples a finite set of actions from the continuous action spaces by a re-sampling mechanism with variable exploratory rates, and the second layer evaluates the actions in the sampled action set and updates the policy using a reinforcement learning cooperative method. By constructing cooperative mechanisms at both levels, SCC-rFMQ can handle cooperative problems in continuous action cooperative Markov games effectively. The effectiveness of SCC-rFMQ is experimentally demonstrated on two well-designed games, i.e., a continuous version of the climbing game and a cooperative version of the boat problem. Experimental results show that SCC-rFMQ outperforms other reinforcement learning algorithms. A large number of multiagent coordination domains involve continuous action spaces, such as robot soccer [1] and multiplayer online battle arena game [2]. In such environments, agents not only need to coordinate with other agents towards desirable outcomes efficiently but also have to deal with infinitely large action spaces.

Ranking is a fundamental and widely studied problem in scenarios such as search, advertising, and recommendation. However, joint optimization for multi-scenario ranking, which aims to improve the overall performance of several ranking strategies in different scenarios, is rather untouched. Separately optimizing each individual strategy has two limitations. The first one is lack of collaboration between scenarios meaning that each strategy maximizes its own objective but ignores the goals of other strategies, leading to a sub-optimal overall performance. The second limitation is the inability of modeling the correlation between scenarios meaning that independent optimization in one scenario only uses its own user data but ignores the context in other scenarios. In this paper, we formulate multi-scenario ranking as a fully cooperative, partially observable, multi-agent sequential decision problem. We propose a novel model named Multi-Agent Recurrent Deterministic Policy Gradient (MA-RDPG) which has a communication component for passing messages, several private actors (agents) for making actions for ranking, and a centralized critic for evaluating the overall performance of the co-working actors. Each scenario is treated as an agent (actor). Agents collaborate with each other by sharing a global action-value function (the critic) and passing messages that encodes historical information across scenarios. The model is evaluated with online settings on a large E-commerce platform. Results show that the proposed model exhibits significant improvements against baselines in terms of the overall performance.

In Multi-Agent Reinforcement Learning, independent cooperative learners must overcome a number of pathologies in order to learn optimal joint policies. These pathologies include action-shadowing, stochasticity, the moving target and alter-exploration problems (Matignon, Laurent, and Le Fort-Piat 2012; Wei and Luke 2016). Numerous methods have been proposed to address these pathologies, but evaluations are predominately conducted in repeated strategic-form games and stochastic games consisting of only a small number of state transitions. This raises the question of the scalability of the methods to complex, temporally extended, partially observable domains with stochastic transitions and rewards. In this paper we study such complex settings, which require reasoning over long time horizons and confront agents with the curse of dimensionality. To deal with the dimensionality, we adopt a Multi-Agent Deep Reinforcement Learning (MA-DRL) approach. We find that when the agents have to make critical decisions in seclusion, existing methods succumb to a combination of relative overgeneralisation (a type of action shadowing), the alter-exploration problem, and the stochasticity. To address these pathologies we introduce expanding negative update intervals that enable independent learners to establish the near-optimal average utility values for higher-level strategies while largely discarding transitions from episodes that result in mis-coordination. We evaluate Negative Update Intervals Double-DQN (NUI-DDQN) within a temporally extended Climb Game, a normal form game which has frequently been used to study relative over-generalisation and other pathologies. We show that NUI-DDQN can converge towards optimal joint-policies in deterministic and stochastic reward settings, overcoming relative-overgeneralisation and the alter-exploration problem while mitigating the moving target problem.

We address item relocation problems in graphs in this paper. We assume items placed in vertices of an undirected graph with at most one item per vertex. Items can be moved across edges while various constraints depending on the type of relocation problem must be satisfied. We introduce a general problem formulation that encompasses known types of item relocation problems such as multi-agent path finding (MAPF) and token swapping (TSWAP). In this formulation we express two new types of relocation problems derived from token swapping that we call token rotation (TROT) and token permutation (TPERM). Our solving approach for item relocation combines satisfiability modulo theory (SMT) with conflict-based search (CBS). We interpret CBS in the SMT framework where we start with the basic model and refine the model with a collision resolution constraint whenever a collision between items occurs in the current solution. The key difference between the standard CBS and our SMT-based modification of CBS (SMT-CBS) is that the standard CBS branches the search to resolve the collision while in SMT-CBS we iteratively add a single disjunctive collision resolution constraint. Experimental evaluation on several benchmarks shows that the SMT-CBS algorithm significantly outperforms the standard CBS. We also compared SMT-CBS with a modification of the SAT-based MDD-SAT solver that uses an eager modeling of item relocation in which all potential collisions are eliminated by constrains in advance. Experiments show that lazy approach in SMT-CBS produce fewer constraint than MDD-SAT and also achieves faster solving run-times.

Specialization and hierarchical organization are important features of efficient collaboration in economical, artificial, and biological systems. Here, we investigate the hypothesis that both features can be explained by the fact that each entity of such a system is limited in a certain way. We propose an information-theoretic approach based on a Free Energy principle, in order to computationally analyze systems of bounded rational agents that deal with such limitations optimally. We find that specialization allows to focus on fewer tasks, thus leading to a more efficient execution, but in turn requires coordination in hierarchical structures of specialized experts and coordinating units. Our results suggest that hierarchical architectures of specialized units at lower levels that are coordinated by units at higher levels are optimal, given that each unit's information-processing capability is limited and conforms to constraints on complexity costs.