Quantum information processing is at the crossroads of physics, mathematics and computer science. It is concerned with what we can and cannot do with quantum information that goes beyond the abilities of classical information processing devices. Communication complexity is an area of classical computer science that aims at quantifying the amount of communication necessary to solve distributed computational problems. Quantum communication complexity uses quantum mechanics to reduce the amount of communication that would be classically required.
There are other pseudo-telepathy games that are related to the magic square game. Ad 'an Cabello's game @cite_31 @cite_26 does not resembles the magic square game on first approach. However, closer analysis reveals that the two games are totally equivalent!
@cite_31 @cite_26
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(2016) introduced the notion of a pseudo-count, derived from a density model, to generalize count-based exploration to non-tabular reinforcement learning. This pseudo-count was used to generate an exploration bonus for a DQN agent and combined with a mixed Monte Carlo update was sufficient to achieve state of the art on the Atari 2600 game Montezuma's Revenge. We consider two questions left open by their work: First, how important is the quality of the density model for exploration? Second, what role does the Monte Carlo update play in exploration? We answer the first question by demonstrating the use of PixelCNN, an advanced neural density model for images, to supply a pseudo-count. In particular, we examine the intrinsic difficulties in adapting 's approach when assumptions about the model are violated. The result is a more practical and general algorithm requiring no special apparatus. We combine PixelCNN pseudo-counts with different agent architectures to dramatically improve the state of the art on several hard Atari games. One surprising finding is that the mixed Monte Carlo update is a powerful facilitator of exploration in the sparsest of settings, including Montezuma's Revenge. Bell inequality violations correspond to behavior of entangled quantum systems that cannot be simulated classically. We give two new two-player games with Bell inequality violations that are stronger, fully explicit, and arguably simpler than earlier work.The first game is based on the Hidden Matching problem of quantum communication complexity, introduced by Bar-Yossef, Jayram, and Kerenidis. This game can be won with probability 1 by a quantum strategy using a maximally entangled state with local dimension n (e.g., log n EPR-pairs), while we show that the winning probability of any classical strategy differs from 1 2 by at most O(log(n) sqrt(n)).The second game is based on the integrality gap for Unique Games by Khot and Vishnoi and the quantum rounding procedure of Kempe, Regev, and Toner. Here n-dimensional entanglement allows to win the game with probability 1 (log n)^2, while the best winning probability without entanglement is 1 n. This near-linear ratio ( Bell inequality violation'') is near-optimal, both in terms of the local dimension of the entangled state, and in terms of the number of possible outputs of the two players. We study the connection between pebble games and complexity. First, we derive complexity results using pebble games. It is shown that three pebble games used for studying computational complexity are equivalent: namely, the two-person pebble game of Dymond-Tompa, the two-person pebble game of Raz-McKenzie, and the one-person reversible pebble game of Bennett have the same pebble costs over any directed acyclic graph. The three pebble games have been used for studying parallel complexity and for proving lower bounds under restricted settings, and we show one more such lower bound on circuit-depth. Second, the pebble costs are applied to proof complexity. Concerning a family of unsatisfiable CNFs called pebbling contradictions, the pebble cost in any of the pebble games controls the scaling of some parameters of resolution refutations. Namely, the pebble cost controls the minimum depth of resolution refutations and the minimum size of tree-like resolution refutations. Finally, we study the space complexity of computing the pebble costs and of computing the minimum depth of resolution refutations. It is PSPACE-complete to compute the pebble cost in any of the three pebble games, and to compute the minimum depth of resolution refutations. Pseudo-random number generation on the Atari 2600 was commonly accomplished using a Linear Feedback Shift Register (LFSR). One drawback was that the initial seed for the LFSR had to be hard-coded into the ROM. To overcome this constraint, programmers sampled from the LFSR once per frame, including title and end screens. Since a human player will have some random amount of delay between seeing the title screen and starting to play, the LFSR state was effectively randomized at the beginning of the game despite the hard-coded seed. Other games used the player’s actions as a source of randomness. Notable pseudo-random games include Adventure in which a bat randomly steals and hides items around the game world and River Raid which used randomness to make enemy movements less predictable. Relying on the player to provide a source of randomness is not sufficient for computer controlled agents which are capable of memorizing and repeating pre-determined sequences of actions. Ideally, the games themselves would provide stochasticity generated from an external source such as the CPU clock. In practice, this was not an option presented by the hardware. Atari games are deterministic given a fixed policy leading to a set sequence of actions. This article discusses different approaches for adding stochasticity to Atari games and examines how effective each approach is at derailing an agent known to memorize action sequences. Additionally it is the authors’ hope that this article will spark discussion in the community over the following questions: Using a humanoid robot and a simple children's game, we examine the degree to which variations in behavior result in attributions of mental state and intentionality. Participants play the well-known children's game "rock-paper-scissors" against a robot that either plays fairly, or that cheats in one of two ways. In the "verbal cheat" condition, the robot announces the wrong outcome on several rounds which it loses, declaring itself the winner. In the "action cheat"' condition, the robot changes its gesture after seeing its opponent's play. We find that participants display a greater level of social engagement and make greater attributions of mental state when playing against the robot in the conditions in which it cheats. DeepMind's recent spectacular success in using deep convolutional neural nets and machine learning to build superhuman level agents --- e.g. for Atari games via deep Q-learning and for the game of Go via Reinforcement Learning --- raises many questions, including to what extent these methods will succeed in other domains. In this paper we consider DQL for the game of Hex: after supervised initialization, we use selfplay to train NeuroHex, an 11-layer CNN that plays Hex on the 13x13 board. Hex is the classic two-player alternate-turn stone placement game played on a rhombus of hexagonal cells in which the winner is whomever connects their two opposing sides. Despite the large action and state space, our system trains a Q-network capable of strong play with no search. After two weeks of Q-learning, NeuroHex achieves win-rates of 20.4 as first player and 2.1 as second player against a 1-second move version of MoHex, the current ICGA Olympiad Hex champion. Our data suggests further improvement might be possible with more training time. Background: The application of digital games for training medical professionals is on the rise. So-called ‘serious’ games form training tools that provide a challenging simulated environment, ideal for future surgical training. Ultimately, serious games are directed at reducing medical error and subsequent healthcare costs. The aim was to review current serious games for training medical professionals and to evaluate the validity testing of such games. Methods: PubMed, Embase, the Cochrane Database of Systematic Reviews, PsychInfo and CINAHL were searched using predefined inclusion criteria for available studies up to April 2012. The primary endpoint was validation according to current criteria. Results: A total of 25 articles were identified, describing a total of 30 serious games. The games were divided into two categories: those developed for specific educational purposes (17) and commercial games also useful for developing skills relevant to medical personnel (13). Pooling of data was not performed owing to the heterogeneity of study designs and serious games. Six serious games were identified that had a process of validation. Of these six, three games were developed for team training in critical care and triage, and three were commercially available games applied to train laparoscopic psychomotor skills. None of the serious games had completed a full validation process for the purpose of use. Conclusion: Blended and interactive learning by means of serious games may be applied to train both technical and non-technical skills relevant to the surgical field. Games developed or used for this purpose need validation before integration into surgical teaching curricula. We give simple proofs of refinements of the complexity results of Gilboa and Zemel (1989), and we derive additional results of this sort. Our constructions employ imitation games, which are two person games in which both players have the same sets of pure strategies and the second player wishes to play the same pure strategy as the first player. We introduce quantum XOR games, a model of two-player, one-round games that extends the model of XOR games by allowing the referee’s questions to the players to be quantum states. We give examples showing that quantum XOR games exhibit a wide range of behaviors that are known not to exist for standard XOR games, such as cases in which the use of entanglement leads to an arbitrarily large advantage over the use of no entanglement. By invoking two deep extensions of Grothendieck’s inequality, we present an efficient algorithm that gives a constant-factor approximation to the best performance that players can obtain in a given game, both in the case that they have no shared entanglement and that they share unlimited entanglement. As a byproduct of the algorithm, we prove some additional interesting properties of quantum XOR games, such as the fact that sharing a maximally entangled state of arbitrary dimension gives only a small advantage over having no entanglement at all. We propose a simple yet rich model to extend strategic games to the quantum setting, in which we define quantum Nash and correlated equilibria and study the relations between classical and quantum equilibria. Unlike all previous work that focused on qualitative questions on specific games of very small sizes, we quantitatively address the following fundamental question for general games of growing sizes: How much "advantage" can playing quantum strategies provide, if any? Two measures of the advantage are studied. 1. Since game mainly is about each player trying to maximize individual payoff, a natural measure is the increase of payoff by playing quantum strategies. We consider natural mappings between classical and quantum states, and study how well those mappings preserve equilibrium properties. Among other results, we exhibit a correlated equilibrium p whose quantum superposition counterpart [EQUATION] is far from being a quantum correlated equilibrium; actually a player can increase her payoff from almost 0 to almost 1 in a [0, 1]-normalized game. We achieve this by a tensor product construction on carefully designed base cases. The result can also be interpreted as in Meyer's comparison [47]: In a state no classical player can gain, one player using quantum computers has an huge advantage than continuing to play classically. 2. Another measure is the hardness of generating correlated equilibria, for which we propose to study correlation complexity, a new complexity measure for correlation generation. We show that there are n-bit correlated equilibria which can be generated by only one EPR pair followed by local operation (without communication), but need at least log2(n) classical shared random bits plus communication. The randomized lower bound can be improved to n, the best possible, assuming (even a much weaker version of) a recent conjecture in linear algebra. We believe that the correlation complexity, as a complexity-theoretical counterpart of the celebrated Bell's inequality, has independent interest in both physics and computational complexity theory and deserves more explorations. Games are used to evaluate and advance Multiagent and Artificial Intelligence techniques. Most of these games are deterministic with perfect information (e.g. Chess and Checkers). A deterministic game has no chance element and in a perfect information game, all information is visible to all players. However, many real-world scenarios with competing agents are stochastic (non-deterministic) with imperfect information. For two-player zero-sum perfect recall games, a recent technique called Counterfactual Regret Minimization (CFR) computes strategies that are provably convergent to an e-Nash equilibrium. A Nash equilibrium strategy is useful in two-player games since it maximizes its utility against a worst-case opponent. However, for multiplayer (three or more player) games, we lose all theoretical guarantees for CFR. However, we believe that CFR-generated agents may perform well in multiplayer games. To test this hypothesis, we used this technique to create several 3-player limit Texas Hold'em poker agents and two of them placed first and second in the 3-player event of the 2009 AAAI IJCAI Computer Poker Competition. We also demonstrate that good strategies can be obtained by grafting sets of two-player subgame strategies to a 3-player base strategy after one of the players is eliminated. We present a novel approach to player modeling based on a convolutional neural net trained on game event logs. We test our approach and a hybrid extension over two distinct games, a clone of Super Mario Bros. and Gwario, a human computation version of Super Mario Bros.: The Lost Levels. We demonstrate high accuracy in predicting a variety of measures of player experience across these two games. Further we present evidence that our technique derives quality design knowledge and demonstrate the ability to build a more general model. We present a protocol that transforms any quantum multi-prover interactive proof into a nonlocal game in which questions consist of logarithmic number of bits and answers of constant number of bits. As a corollary, it follows that the promise problem corresponding to the approximation of the nonlocal value to inverse polynomial accuracy is complete for QMIP*, and therefore NEXP-hard. This establishes that nonlocal games are provably harder than classical games without any complexity theory assumptions. Our result also indicates that gap amplification for nonlocal games may be impossible in general and provides a negative evidence for the feasibility of the gap amplification approach to the multi-prover variant of the quantum PCP conjecture. We consider an agent's uncertainty about its environment and the problem of generalizing this uncertainty across states. Specifically, we focus on the problem of exploration in non-tabular reinforcement learning. Drawing inspiration from the intrinsic motivation literature, we use density models to measure uncertainty, and propose a novel algorithm for deriving a pseudo-count from an arbitrary density model. This technique enables us to generalize count-based exploration algorithms to the non-tabular case. We apply our ideas to Atari 2600 games, providing sensible pseudo-counts from raw pixels. We transform these pseudo-counts into exploration bonuses and obtain significantly improved exploration in a number of hard games, including the infamously difficult MONTEZUMA'S REVENGE. We show that setting a reasonable frame skip can be critical to the performance of agents learning to play Atari 2600 games. In all of the six games in our experiments, frame skip is a strong determinant of success. For two of these games, setting a large frame skip leads to state-of-the-art performance. The rate at which an agent interacts with its environment may be critical to its success. In the Arcade Learning Environment (ALE) ( 2013) games run at sixty frames per second, and agents can submit an action at every frame. Frame skip is the number of frames an action is repeated before a new action is selected. Existing reinforcement learning (RL) approaches use static frame skip: HNEAT ( 2013) uses a frame skip of 0; DQN ( 2013) uses a frame skip of 2-3; SARSA and planning approaches ( 2013) use a frame skip of 4. When action selection is computationally intensive, setting a higher frame skip can significantly decrease the time it takes to simulate an episode, at the cost of missing opportunities that only exist at a finer resolution. A large frame skip can also prevent degenerate super-human-reflex strategies, such as those described by for Bowling, Kung Fu Master, Video Pinball and Beam Rider. We show that in addition to these advantages agents that act with high frame skip can actually learn faster with respect to the number of training episodes than those that skip no frames. We present results for six of the seven games covered by : three (Beam Rider, Breakout and Pong) for which DQN was able to achieve near- or superhuman performance, and three (Q*Bert, Space Invaders and Seaquest) for which all RL approaches are far from human performance. These latter games were understood to be difficult because they require ‘strategy that extends over long time scales.’ In our experiments, setting a large frame skip was critical to achieving state-of-the-art performance in two of these games: Space Invaders and Q*Bert. More generally, the frame skip parameter was a strong determinant of performance in all six games. Our learning framework is a variant of Enforced Subpopulations (ESP) (Gomez and Miikkulainen 1997), a neuroevolution approach that has been successfully imple We solve Conway's Angel Problem by showing that the Angel of power 2 has a winning strategy. An old observation of Conway is that we may suppose without loss of generality that the Angel never jumps to a square where he could have already landed at a previous time. We turn this observation around and prove that we may suppose without loss of generality that the Devil never eats a square where the Angel could have already jumped. Then we give a simple winning strategy for the Angel. Simple coalitional games are a fundamental class of cooperative games and voting games which are used to model coalition formation, resource allocation and decision making in computer science, artificial intelligence and multiagent systems. Although simple coalitional games are well studied in the domain of game theory and social choice, their algorithmic and computational complexity aspects have received less attention till recently. The computational aspects of simple coalitional games are of increased importance as these games are used by computer scientists to model distributed settings. This thesis fits in the wider setting of the interplay between economics and computer science which has led to the development of algorithmic game theory and computational social choice. A unified view of the computational aspects of simple coalitional games is presented here for the first time. Certain complexity results also apply to other coalitional games such as skill games and matching games. The following issues are given special consideration: influence of players, limit and complexity of manipulations in the coalitional games and complexity of resource allocation on networks. The complexity of comparison of influence between players in simple games is characterized. The simple games considered are represented by winning coalitions, minimal winning coalitions, weighted voting games or multiple weighted voting games. A comprehensive classification of weighted voting games which can be solved in polynomial time is presented. An efficient algorithm which uses generating functions and interpolation to compute an integer weight vector for target power indices is proposed. Voting theory, especially the Penrose Square Root Law, is used to investigate the fairness of a real life voting model. Computational complexity of manipulation in social choice protocols can determine whether manipulation is computationally feasible or not. The computational complexity and bounds of manipulation are considered from various angles including control, false-name manipulation and bribery. Moreover, the computational complexity of computing various cooperative game solutions of simple games in dierent representations is studied. Certain structural results regarding least core payos extend to the general monotone cooperative game. The thesis also studies a coalitional game called the spanning connectivity game. It is proved that whereas computing the Banzhaf values and Shapley-Shubik indices of such games is #P-complete, there is a polynomial time combinatorial algorithm to compute the nucleolus. The results have interesting significance for optimal strategies for the wiretapping game which is a noncooperative game defined on a network. We consider an agent's uncertainty about its environment and the problem of generalizing this uncertainty across observations. Specifically, we focus on the problem of exploration in non-tabular reinforcement learning. Drawing inspiration from the intrinsic motivation literature, we use density models to measure uncertainty, and propose a novel algorithm for deriving a pseudo-count from an arbitrary density model. This technique enables us to generalize count-based exploration algorithms to the non-tabular case. We apply our ideas to Atari 2600 games, providing sensible pseudo-counts from raw pixels. We transform these pseudo-counts into intrinsic rewards and obtain significantly improved exploration in a number of hard games, including the infamously difficult Montezuma's Revenge. An imitation game is a finite two person normal form game in which the two players have the same set of pure strategies and the goal of the second player is to choose the same pure strategy as the first player. We explain how, in two different settings, observations obtained from imitation games complete a circle of ideas, showing that phenomena that had for many years seemed to be distinct are actually superficially different manifestations of a single structure. First, one can pass from a given two person finite game to an imitation game whose Nash equilibria are in one-to-one correspondence with the Nash equilibria of the given game. Second, each of the paths of the procedure described in Lemke (1965) for solving a linear complementarity problem is the projection of the path of the Lemke-Howson algorithm applied to an imitation game. We construct a linear system non-local game which can be played perfectly using a limit of finite-dimensional quantum strategies, but which cannot be played perfectly on any finite-dimensional Hilbert space, or even with any tensor-product strategy. In particular, this shows that the set of (tensor-product) quantum correlations is not closed. The constructed non-local game provides another counterexample to the "middle" Tsirelson problem, with a shorter proof than our previous paper (though at the loss of the universal embedding theorem). We also show that it is undecidable to determine if a linear system game can be played perfectly with a finite-dimensional strategy, or a limit of finite-dimensional quantum strategies.