Behavioral game theory seeks to describe the way actual people (as compared to idealized, "rational" agents) act in strategic situations. Our own recent work has identified iterative models, such as quantal cognitive hierarchy, as the state of the art for predicting human play in unrepeated, simultaneous-move games. Iterative models predict that agents reason iteratively about their opponents, building up from a specification of nonstrategic behavior called level-0. A modeler is in principle free to choose any description of level-0 behavior that makes sense for a given setting. However, in practice almost all existing work specifies this behavior as a uniform distribution over actions. In most games it is not plausible that even nonstrategic agents would choose an action uniformly at random, nor that other agents would expect them to do so. A more accurate model for level-0 behavior has the potential to dramatically improve predictions of human behavior, since a substantial fraction of agents may play level-0 strategies directly, and furthermore since iterative models ground all higher-level strategies in responses to the level-0 strategy. Our work considers models of the way in which level-0 agents construct a probability distribution over actions, given an arbitrary game. We considered a large space of alternatives and, in the end, recommend a model that achieved excellent performance across the board: a linear weighting of four binary features, each of which is general in the sense that it can be computed from any normal form game. Adding real-valued variants of the same four features yielded further improvements in performance, albeit with a corresponding increase in the number of parameters needing to be estimated. We evaluated the effects of combining these new level-0 models with several iterative models and observed large improvements in predictive accuracy.

Humans use language to collectively execute complex strategies in addition to using it as a referential tool for referring to physical entities. While existing approaches that study the emergence of language in settings where the language mainly acts as a referential tool, in this paper, we study the role of emergent languages in discovering and implementing strategies in a multi-agent setting. The agents in our setup are connected via a network and are allowed to exchange messages in the form of sequences of discrete symbols. We formulate the problem as a voting game, where two candidate agents are contesting in an election and their goal is to convince the population members (other agents) in the network to vote for them by sending them messages. We use neural networks to parameterize the policies followed by agents in the game. We investigate the effect of choosing different training objectives and strategies for agents in the game and make observations about the emergent language in each case. To the best of our knowledge this is the first work that explores emergence of language for discovering and implementing strategies in a setting where agents are connected via an underlying network.

Consider a network of agents connected by communication links, where each agent holds a real value. The gossip problem consists in estimating the average of the values diffused in the network in a distributed manner. We develop a method solving the gossip problem that depends only on the spectral dimension of the network, that is, in the communication network set-up, the dimension of the space in which the agents live. This contrasts with previous work that required the spectral gap of the network as a parameter, or suffered from slow mixing. Our method shows an important improvement over existing algorithms in the non-asymptotic regime, i.e., when the values are far from being fully mixed in the network. Our approach stems from a polynomial-based point of view on gossip algorithms, as well as an approximation of the spectral measure of the graphs with a Jacobi measure. We show the power of the approach with simulations on various graphs, and with performance guarantees on graphs of known spectral dimension, such as grids and random percolation bonds. An extension of this work to distributed Laplacian solvers is discussed. As a side result, we also use the polynomial-based point of view to show the convergence of the message passing algorithm for gossip of Moallemi \& Van Roy on regular graphs. The explicit computation of the rate of the convergence shows that message passing has a slow rate of convergence on graphs with small spectral gap.

In this paper, we propose a new learning technique named message-dropout to improve the performance for multi-agent deep reinforcement learning under two application scenarios: 1) classical multi-agent reinforcement learning with direct message communication among agents and 2) centralized training with decentralized execution. In the first application scenario of multi-agent systems in which direct message communication among agents is allowed, the message-dropout technique drops out the received messages from other agents in a block-wise manner with a certain probability in the training phase and compensates for this effect by multiplying the weights of the dropped-out block units with a correction probability. The applied message-dropout technique effectively handles the increased input dimension in multi-agent reinforcement learning with communication and makes learning robust against communication errors in the execution phase. In the second application scenario of centralized training with decentralized execution, we particularly consider the application of the proposed message-dropout to Multi-Agent Deep Deterministic Policy Gradient (MADDPG), which uses a centralized critic to train a decentralized actor for each agent. We evaluate the proposed message-dropout technique for several games, and numerical results show that the proposed message-dropout technique with proper dropout rate improves the reinforcement learning performance significantly in terms of the training speed and the steady-state performance in the execution phase.

Limited lookahead has been studied for decades in complete-information games. We initiate a new direction via two simultaneous deviation points: generalization to incomplete-information games and a game-theoretic approach. We study how one should act when facing an opponent whose lookahead is limited. We study this for opponents that differ based on their lookahead depth, based on whether they, too, have incomplete information, and based on how they break ties. We characterize the hardness of finding a Nash equilibrium or an optimal commitment strategy for either player, showing that in some of these variations the problem can be solved in polynomial time while in others it is PPAD-hard or NP-hard. We proceed to design algorithms for computing optimal commitment strategies---for when the opponent breaks ties favorably, according to a fixed rule, or adversarially. We then experimentally investigate the impact of limited lookahead. The limited-lookahead player often obtains the value of the game if she knows the expected values of nodes in the game tree for some equilibrium---but we prove this is not sufficient in general. Finally, we study the impact of noise in those estimates and different lookahead depths. This uncovers an incomplete-information game lookahead pathology.

"We are proud of our cars and so we should be," Merkel said, adding, however, that many were built in the United States and exported to China. "If that is viewed as a security threat to the United States, then we are shocked," she told the Munich Security Conference to applause from the audience.

Deep learning has achieved remarkable successes in solving challenging reinforcement learning (RL) problems when dense reward function is provided. However, in sparse reward environment it still often suffers from the need to carefully shape reward function to guide policy optimization. This limits the applicability of RL in the real world since both reinforcement learning and domain-specific knowledge are required. It is therefore of great practical importance to develop algorithms which can learn from a binary signal indicating successful task completion or other unshaped, sparse reward signals. We propose a novel method called competitive experience replay, which efficiently supplements a sparse reward by placing learning in the context of an exploration competition between a pair of agents. Our method complements the recently proposed hindsight experience replay (HER) by inducing an automatic exploratory curriculum. We evaluate our approach on the tasks of reaching various goal locations in an ant maze and manipulating objects with a robotic arm. Each task provides only binary rewards indicating whether or not the goal is achieved. Our method asymmetrically augments these sparse rewards for a pair of agents each learning the same task, creating a competitive game designed to drive exploration. Extensive experiments demonstrate that this method leads to faster converge and improved task performance.

This technical report documents the winner of the Computational Intelligence in Games(CIG) 2018 Hanabi competition. We introduce Re-determinizing IS-MCTS, a novel extension of Information Set Monte Carlo Tree Search (IS-MCTS) \cite{IS-MCTS} that prevents a leakage of hidden information into opponent models that can occur in IS-MCTS, and is particularly severe in Hanabi. Re-determinizing IS-MCTS scores higher in Hanabi for 2-4 players than previously published work. Given the 40ms competition time limit per move we use a learned evaluation function to estimate leaf node values and avoid full simulations during MCTS. For the Mixed track competition, in which the identity of the other players is unknown, a simple Bayesian opponent model is used that is updated as each game proceeds.

But it's not always practical; model-free approaches, which aim to get agents to directly predict actions from observations about their world, can take weeks of training. Model-based reinforcement learning is a viable alternative -- it has agents come up with a general model of their environment they can use to plan ahead. But in order to accurately forecast actions in unfamiliar surroundings, those agents have to formulate rules from experience. Toward that end, Google in collaboration with DeepMind today introduced the Deep Planning Network (PlaNet) agent, which learns a world model from image inputs and leverages it for planning. It's able to solve a variety of image-based tasks with up to 5,000 percent the data efficiency, Google says, while maintaining competitiveness with advanced model-free agents.

Here we identify a type of privacy concern in Distributed Constraint Optimization (DCOPs) not previously addressed in literature, despite its importance and impact on the application field: the privacy of existence of secrets. Science only starts where metrics and assumptions are clearly defined. The area of Distributed Constraint Optimization has emerged at the intersection of the multi-agent system community and constraint programming. For the multi-agent community, the constraint optimization problems are an elegant way to express many of the problems occurring in trading and distributed robotics. For the theoretical constraint programming community the DCOPs are a natural extension of their main object of study, the constraint satisfaction problem. As such, the understanding of the DCOP framework has been refined with the needs of the two communities, but sometimes without spelling the new assumptions formally and therefore making it difficult to compare techniques. Here we give a direction to the efforts for structuring concepts in this area.