Deterministic-policy actor-critic algorithms for continuous control improve the actor by plugging its actions into the critic and ascending the action-value gradient, which is obtained by chaining the actor's Jacobian matrix with the gradient of the critic with respect to input actions. However, instead of gradients, the critic is, typically, only trained to accurately predict expected returns, which, on their own, are useless for policy optimization. In this paper, we propose MAGE, a model-based actor-critic algorithm, grounded in the theory of policy gradients, which explicitly learns the action-value gradient. MAGE backpropagates through the learned dynamics to compute gradient targets in temporal difference learning, leading to a critic tailored for policy improvement. On a set of MuJoCo continuous-control tasks, we demonstrate the efficiency of the algorithm in comparison to model-free and model-based state-of-the-art baselines.

Efficient exploration is an unsolved problem in Reinforcement Learning which is usually addressed by reactively rewarding the agent for fortuitously encountering novel situations. This paper introduces an efficient active exploration algorithm, Model-Based Active eXploration (MAX), which uses an ensemble of forward models to plan to observe novel events. This is carried out by optimizing agent behaviour with respect to a measure of novelty derived from the Bayesian perspective of exploration, which is estimated using the disagreement between the futures predicted by the ensemble members. We show empirically that in semi-random discrete environments where directed exploration is critical to make progress, MAX is at least an order of magnitude more efficient than strong baselines. MAX scales to high-dimensional continuous environments where it builds task-agnostic models that can be used for any downstream task.

This paper presents the first two editions of Visual Doom AI Competition, held in 2016 and 2017. The challenge was to create bots that compete in a multiplayer deathmatch in a first-person shooter game Doom. The bots had to make their decisions solely based on visual information, i.e., a raw screen buffer. To play well, the bots needed to understand their surroundings, navigate, explore, and handle the opponents at the same time. These aspects, together with the competitive multiagent aspect of the game, make the competition a unique platform for evaluating the state-of-the-art reinforcement learning algorithms. This paper discusses the rules, solutions, results, and statistics that give insight into the agents' behaviors. Best performing agents are described in more detail. The results of the competition lead to the conclusion that, although reinforcement learning can produce capable Doom bots, they still are not yet able to successfully compete against humans in this game. This paper also revisits the ViZDoom environment, which is a flexible, easy to use, and efficient three-dimensional platform for research for vision-based reinforcement learning, based on a well-recognized first-person perspective game Doom.

2048 is an engaging single-player nondeterministic video puzzle game, which, thanks to the simple rules and hard-tomaster gameplay, has gained massive popularity in recent years. As 2048 can be conveniently embedded into the discrete-state Markov decision processes framework, we treat it as a testbed for evaluating existing and new methods in reinforcement learning. With the aim to develop a strong 2048 playing program, we employ temporal difference learning with systematic n-tuple networks. We show that this basic method can be significantly improved with temporal coherence learning, multistage function approximator with weight promotion, carousel shaping, and redundant encoding. In addition, we demonstrate how to take advantage of the characteristics of the n-tuple network, to improve the algorithmic effectiveness of the learning process by delaying the (decayed) update and applying lock-free optimistic parallelism to effortlessly make advantage of multiple CPU cores. This way, we were able to develop the best known 2048 playing program to date, which confirms the effectiveness of the introduced methods for discrete-state Markov decision problems.

Achieving a superhuman playing level by AlphaGo corroborated the capabilities of convolutional neural network (CNN) architectures for capturing complex spatial patterns. This result was, to a great extent, due to several analogies between Go board states and 2-D images that CNNs have been designed for, in particular, translational invariance and a relatively large board. In this paper, we verify whether CNN-based move predictors prove effective for Othello, a game with significantly different characteristics, including a much smaller board size and complete lack of translational invariance. We compare several CNN architectures and board encodings, augment them with state-of-the-art extensions, train on an extensive database of experts' moves, and examine them with respect to move prediction accuracy and playing strength. The empirical evaluation confirms high capabilities of neural move predictors and suggests a strong correlation between prediction accuracy and playing strength. The best CNNs not only surpass all other 1-ply Othello players proposed to date but defeat (2 ply) Edax, the best open-source Othello player.

Among many interaction schemes in coevolutionary settings for interactive domains, the round-robin tournament provides the most precise evaluation of candidate solutions at the expense of computational effort. In order to improve the coevolutionary learning speed, we propose an interaction scheme that computes only a fraction of interactions outcomes between the pairs of coevolving individuals. The missing outcomes in the interaction matrix are predicted using matrix factorization. The algorithm adaptively decides how much of the interaction matrix to compute based on the learning speed statistics. We evaluate our method in the context of coevolutionary covariance matrix adaptation strategy (CoCMAES) for the problem of learning position evaluation in the game of Othello. We show that our adaptive interaction scheme allows to match the state-of-the-art results obtained by the standard round-robin CoCMAES while, at the same time, considerably improves the learning speed.

One weakness of coevolutionary algorithms observed in knowledge-free learning of strategies for adversarial games has been their poor scalability with respect to the number of parameters to learn. In this paper, we investigate to what extent this problem can be mitigated by using Covariance Matrix Adaptation Evolution Strategy, a powerful continuous optimization algorithm. In particular, we employ this algorithm in a competitive coevolutionary setup, denoting this setting as Co-CMA-ES. We apply it to learn position evaluation functions for the game of Othello and find out that, in contrast to plain (co)evolution strategies, Co-CMA-ES learns faster, finds superior game-playing strategies and scales better. Its advantages come out into the open especially for large parameter spaces of tens of hundreds of dimensions. For Othello, combining Co-CMA-ES with experimentally-tuned derandomized systematic n-tuple networks significantly improved the current state of the art. Our best strategy outperforms all the other Othello 1-ply players published to date by a large margin regardless of whether the round-robin tournament among them involves a fixed set of initial positions or the standard initial position but randomized opponents. These results show a large potential of CMA-ES-driven coevolution, which could be, presumably, exploited also in other games.

SZ-Tetris, a restricted version of Tetris, is a difficult reinforcement learning task. Previous research showed that, similarly to the original Tetris, value function-based methods such as temporal difference learning, do not work well for SZ-Tetris. The best performance in this game was achieved by employing direct policy search techniques, in particular the cross-entropy method in combination with handcrafted features. Nonetheless, a simple heuristic hand-coded player scores even higher. Here we show that it is possible to equal its performance with CMA-ES (Covariance Matrix Adaptation Evolution Strategy). We demonstrate that further improvement is possible by employing systematic n-tuple network, a knowledge-free function approximator, and VD-CMA-ES, a linear variant of CMA-ES for high dimension optimization. Last but not least, we show that a large systematic n-tuple network (involving more than 4 million parameters) allows the classical temporal difference learning algorithm to obtain similar average performance to VD-CMA-ES, but at 20 times lower computational expense, leading to the best policy for SZ-Tetris known to date. These results enrich the current understanding of difficulty of SZ-Tetris, and shed new light on the capabilities of particular search paradigms when applied to representations of various characteristics and dimensionality.

Recent developments cast doubts on the effectiveness of coevolutionary learning in interactive domains. A simple evolution with fitness evaluation based on games with random strategies has been found to generalize better than competitive coevolution. In an attempt to investigate this phenomenon, we analyze the utility of random opponents for one and two-population competitive coevolution applied to learning strategies for the game of Othello. We show that if coevolution uses two-population setup and engages also random opponents, it is capable of producing equally good strategies as evolution with random sampling for the expected utility performance measure. To investigate the differences between analyzed methods, we introduce performance profile, a tool that measures the player's performance against opponents of various strength. The profiles reveal that evolution with random sampling produces players coping well with mediocre opponents, but playing relatively poorly against stronger ones. This finding explains why in the round-robin tournament, evolution with random sampling is one of the worst methods from all those considered in this study.

In evolutionary learning of game-playing strategies, fitness evaluation is based on playing games with certain opponents. In this paper we investigate how the performance of these opponents and the way they are chosen influence the efficiency of learning. For this purpose we introduce a simple method for shaping the fitness function by sampling the opponents from a biased performance distribution. We compare the shaped function with existing fitness evaluation approaches that sample the opponents from an unbiased performance distribution or from a coevolving population. In an extensive computational experiment we employ these methods to learn Othello strategies and assess both the absolute and relative performance of the elaborated players. The results demonstrate the superiority of the shaping approach, and can be explained by means of performance profiles, an analytical tool that evaluate the evolved strategies using a range of variably skilled opponents.

This study investigates different methods of learning to play the game of Othello. The main questions posed concern scalability of algorithms with respect to the search space size and their capability to generalize and produce players that fare well against various opponents. The considered algorithms represent strategies as n-tuple networks, and employ self-play temporal difference learning (TDL), evolutionary learning (EL) and coevolutionary learning (CEL), and hybrids thereof. To assess the performance, three different measures are used: score against an a priori given opponent (a fixed heuristic strategy), against opponents trained by other methods (round-robin tournament), and against the top-ranked players from the online Othello League. We demonstrate that although evolutionary-based methods yield players that fare best against a fixed heuristic player, it is the coevolutionary temporal difference learning (CTDL), a hybrid of coevolution and TDL, that generalizes better and proves superior when confronted with a pool of previously unseen opponents. Moreover, CTDL scales well with the size of representation, attaining better results for larger n-tuple networks. By showing that a strategy learned in this way wins against the top entries from the Othello League, we conclude that it is one of the best 1-ply Othello players obtained to date without explicit use of human knowledge.

Genetic programming (GP) is not a field noted for the rigor of its benchmarking. Some of its benchmark problems are popular purely through historical contingency, and they can be criticized as too easy or as providing misleading information concerning real-world performance, but they persist largely because of inertia and the lack of good alternatives. Even where the problems themselves are impeccable, comparisons between studies are made more difficult by the lack of standardization. We argue that the definition of standard benchmarks is an essential step in the maturation of the field. We make several contributions towards this goal. We motivate the development of a benchmark suite and define its goals; we survey existing practice; we enumerate many candidate benchmarks; we report progress on reference implementations; and we set out a concrete plan for gathering feedback from the GP community that would, if adopted, lead to a standard set of benchmarks.

Problems in which some elementary entities interact with each other are common in computational intelligence. This scenario, typical for coevolving artificial life agents, learning strategies for games, and machine learning from examples, can be formalized as a test-based problem and conveniently embedded in the common conceptual framework of coevolution. In test-based problems, candidate solutions are evaluated on a number of test cases (agents, opponents, examples). It has been recently shown that every test of such problem can be regarded as a separate objective, and the whole problem as multi-objective optimization. Research on reducing the number of such objectives while preserving the relations between candidate solutions and tests led to the notions of underlying objectives and internal problem structure, which can be formalized as a coordinate system that spatially arranges candidate solutions and tests. The coordinate system that spans the minimal number of axes determines the so-called dimension of a problem and, being an inherent property of every problem, is of particular interest. In this study, we investigate in-depth the formalism of a coordinate system and its properties, relate them to properties of partially ordered sets, and design an exact algorithm for finding a minimal coordinate system. We also prove that this problem is NP-hard and come up with a heuristic which is superior to the best algorithm proposed so far. Finally, we apply the algorithms to three abstract problems and demonstrate that the dimension of the problem is typically much lower than the number of tests, and for some problems converges to the intrinsic parameter of the problem--its a priori dimension.

Problems in which some entities interact with each other are common in computational intelligence. This scenario, typical for co-evolving artificial-life agents, learning strategies for games, and machine learning from examples, can be formalized as test-based problem. In test-based problems, candidate solutions are evaluated on a number of test cases (agents, opponents, examples). It has been recently shown that at least some of such problems posses underlying problem structure, which can be formalized in a notion of coordinate system, which spatially arranges candidate solutions and tests in a multidimensional space. Such a coordinate system can be extracted to reveal underlying objectives of the problem, which can be then further exploited to help coevolutionary algorithm make progress. In this study, we propose a novel coevolutionary archive method, called Coordinate System Archive (COSA) that is based on these concepts. In the experimental part, we compare COSA to two state-of-the-art archive methods, IPCA and LAPCA. Using two different objective performance measures, we find out that COSA is superior to these methods on a class of artificial problems (COMPARE-ON-ONE).

In evolutionary algorithms, the typical post-processing phase involves selection of the best-of-run individual, which becomes the final outcome of the evolutionary run. Trivial for deterministic problems, this task can get computationally demanding in noisy environments. A typical naive procedure used in practice is to repeat the evaluation of each individual for the fixed number of times and select the one with the highest average. In this paper, we consider several algorithms that can adaptively choose individuals to evaluate basing on the results evaluations which have already been performed. The procedures are designed without any specific assumption about noise distribution. In the experimental part, we compare our algorithms with the naive and optimal procedures, and find out that the performance of typically used naive algorithm is poor even for relatively moderate noise. We also show that one of our algorithms is nearly optimal for most of the examined situations.

We introduce fitnessless coevolution (FC), a novel method of comparative one-population coevolution. FC plays games between individuals to settle tournaments in the selection phase and skips the typical phase of evaluation. The selection operator applies a single-elimination tournament to a randomly drawn group of individuals, and the winner of the final round becomes the result of selection. Therefore, FC does not involve explicit fitness measure. We prove that, under a condition of transitivity of the payoff matrix, the dynamics of FC is identical to that of the traditional evolutionary algorithm. The experimental results, obtained on a diversified group of problems, demonstrate that FC is able to produce solutions that are equally good or better than solutions obtained using fitness-based one-population coevolution with different selection methods.

This work introduces a numerical, continuous measure of symmetry for 3D stick creatures and solid 3D objects. Background information about the property of symmetry is provided, and motivations for developing a symmetry measure are described. Three approaches are mentioned, and two of them are presented in detail using formal mathematical language. The best approach is used to sort a set of creatures according to their symmetry. Experiments with a mixed set of 84 individuals originating from both human design and evolution are performed to examine symmetry within these two sources, and to determine if human designers and evolutionary processes prefer symmetry or asymmetry.

We propose a multitask learning method of visual concepts within the genetic programming (GP) framework. Each GP individual is composed of several trees that process visual primitives derived from input images. Two trees solve two different visual tasks and are allowed to share knowledge with each other by commonly calling the remaining GP trees (subfunctions) included in the same individual. The performance of a particular tree is measured by its ability to reproduce the shapes contained in the training images. We apply this method to visual learning tasks of recognizing simple shapes and compare it to a reference method. The experimental verification demonstrates that such multitask learning often leads to performance improvements in one or both solved tasks, without extra computational effort.

We consider multitask learning of visual concepts within genetic programming (GP) framework. The proposed method evolves a population of GP individuals, with each of them composed of several GP trees that process visual primitives derived from input images. The two main trees are delegated to solving two different visual tasks and are allowed to share knowledge with each other by calling the remaining GP trees (subfunctions) included in the same individual. The method is applied to the visual learning task of recognizing simple shapes, using generative approach based on visual primitives. We compare this approach to a reference method devoid of knowledge sharing, and conclude that in the worst case cross-task learning performs equally well, and in many cases it leads to significant performance improvements in one or both solved tasks.

We propose a method of knowledge reuse for an ensemble of genetic programming-based learners solving a visual learning task. First, we introduce a visual learning method that uses genetic programming individuals to represent hypotheses. Individuals-hypotheses process image representation composed of visual primitives derived from the training images that contain objects to be recognized. The process of recognition is generative, i.e., an individual is supposed to restore the shape of the processed object by drawing its reproduction on a separate canvas. This canonical method is extended with a knowledge reuse mechanism that allows a learner to import genetic material from hypotheses that evolved for the other decision classes (object classes). We compare the performance of the extended approach to the basic method on a real-world tasks of handwritten character recognition, and conclude that knowledge reuse leads to significant convergence speedup and, more importantly, significantly reduces the risk of overfitting.