Wojciech Jaśkowski

Better GP benchmarks: community survey results and proposals

We present the results of a community survey regarding genetic programming benchmark practices. Analysis shows broad consensus that improvement is needed in problem selection and experimental rigor. While views expressed in the survey dissuade us from proposing a large-scale benchmark suite, we find community support for creating a “blacklist” of problems which are in common use but have important flaws, and whose use should therefore be discouraged. We propose a set of possible replacement problems.

Improving coevolution by random sampling

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 players 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.

Evolving strategy for a probabilistic game of imperfect information using genetic programming

We provide the complete record of methodology that let us evolve BrilliAnt, the winner of the Ant Wars contest. Ant Wars contestants are virtual ants collecting food on a grid board in the presence of a competing ant. BrilliAnt has been evolved through a competitive one-population coevolution using genetic programming and fitnessless selection. In this paper, we detail the evolutionary setup that lead to BrilliAnt’s emergence, assess its direct and indirect human-competitiveness, and describe the behavioral patterns observed in its strategy.

Evolving small-board Go players using coevolutionary temporal difference learning with archives

Evolving small-board Go players using coevolutionary temporal difference learning with archives We apply Coevolutionary Temporal Difference Learning (CTDL) to learn small-board Go strategies represented as weighted piece counters. CTDL is a randomized learning technique which interweaves two search processes that operate in the intra-game and inter-game mode. Intra-game learning is driven by gradient-descent Temporal Difference Learning (TDL), a reinforcement learning method that updates the board evaluation function according to differences observed between its values for consecutively visited game states. For the inter-game learning component, we provide a coevolutionary algorithm that maintains a sample of strategies and uses the outcomes of games played between them to iteratively modify the probability distribution, according to which new strategies are generated and added to the sample. We analyze CTDLs sensitivity to all important parameters, including the trace decay constant that controls the lookahead horizon of TDL, and the relative intensity of intra-game and inter-game learning. We also investigate how the presence of memory (an archive) affects the search performance, and find out that the archived approach is superior to other techniques considered here and produces strategies that outperform a handcrafted weighted piece counter strategy and simple liberty-based heuristics. This encouraging result can be potentially generalized not only to other strategy representations used for small-board Go, but also to various games and a broader class of problems, because CTDL is generic and does not rely on any problem-specific knowledge.

Formal analysis, hardness, and algorithms for extracting internal structure of test-based problems

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.

Learning and Recognition of Hand-Drawn Shapes Using Generative Genetic Programming

We describe a novel method of evolutionary visual learning that uses generative approach for assessing learners ability to recognize image contents. Each learner, implemented as a genetic programming individual, processes visual primitives that represent local salient features derived from a raw input raster image. In response to that input, the learner produces partial reproduction of the input image, and is evaluated according to the quality of that reproduction. We present the method in detail and verify it experimentally on the real-world task of recognition of hand-drawn shapes.

The numerical measure of symmetry for 3d stick creatures

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.

High-Dimensional Function Approximation for Knowledge-Free Reinforcement Learning: a Case Study in SZ-Tetris

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.

Fitnessless coevolution

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.

Multitask visual learning using genetic programming

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.