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Register a new userAlternative Restart Strategies for CMA-ES
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Loshchilov Ilya
Publication date
2012
fields
Informatics Engineering
and research's language is
English
Authors
Ilya Loshchilov
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This paper focuses on the restart strategy of CMA-ES on multi-modal functions. A first alternative strategy proceeds by decreasing the initial step-size of the mutation while doubling the population size at each restart. A second strategy adaptively allocates the computational budget among the restart settings in the BIPOP scheme. Both restart strategies are validated on the BBOB benchmark; their generality is also demonstrated on an independent real-world problem suite related to spacecraft trajectory optimization.
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We propose a computationally efficient limited memory Covariance Matrix Adaptation Evolution Strategy for large scale optimization, which we call the LM-CMA-ES. The LM-CMA-ES is a stochastic, derivative-free algorithm for numerical optimization of non-linear, non-convex optimization problems in continuous domain. Inspired by the limited memory BFGS method of Liu and Nocedal (1989), the LM-CMA-ES samples candidate solutions according to a covariance matrix reproduced from $m$ direction vectors selected during the optimization process. The decomposition of the covariance matrix into Cholesky factors allows to reduce the time and memory complexity of the sampling to $O(mn)$, where $n$ is the number of decision variables. When $n$ is large (e.g., $n$ > 1000), even relatively small values of $m$ (e.g., $m=20,30$) are sufficient to efficiently solve fully non-separable problems and to reduce the overall run-time.
The Covariance Matrix Adaptation Evolution Strategy (CMA-ES) is widely accepted as a robust derivative-free continuous optimization algorithm for non-linear and non-convex optimization problems. CMA-ES is well known to be almost parameterless, meaning that only one hyper-parameter, the population size, is proposed to be tuned by the user. In this paper, we propose a principled approach called self-CMA-ES to achieve the online adaptation of CMA-ES hyper-parameters in order to improve its overall performance. Experimental results show that for larger-than-default population size, the default settings of hyper-parameters of CMA-ES are far from being optimal, and that self-CMA-ES allows for dynamically approaching optimal settings.
Over the past few years the Angry Birds AI competition has been held in an attempt to develop intelligent agents that can successfully and efficiently solve levels for the video game Angry Birds. Many different agents and strategies have been developed to solve the complex and challenging physical reasoning problems associated with such a game. However none of these agents attempt one of the key strategies which humans employ to solve Angry Birds levels, which is restarting levels. Restarting is important in Angry Birds because sometimes the level is no longer solvable or some given shot made has little to no benefit towards the ultimate goal of the game. This paper proposes a framework and experimental evaluation for when to restart levels in Angry Birds. We demonstrate that restarting is a viable strategy to improve agent performance in many cases.
Common research tasks ask students to identify a correct answer and justify their answer choice. We propose expanding the array of research tasks to access different knowledge that students might have. By asking students to discuss answers they may not have chosen naturally, we can investigate students abilities to explain something that is already established or to disprove an incorrect response. The results of these research tasks also provide us with information about how students responses vary across the different tasks. We discuss three underused question types, their possible benefits and some preliminary results from an electric circuits pretest utilizing these new question types. We find that the answer students most commonly choose as correct is the same choice most commonly eliminated as incorrect. Also, students given the correct answer can provide valuable reasoning to explain it, but they do not spontaneously identify it as the correct answer.
Current implementations of pseudo-Boolean (PB) solvers working on native PB constraints are based on the CDCL architecture which empowers highly efficient modern SAT solvers. In particular, such PB solvers not only implement a (cutting-planes-based) conflict analysis procedure, but also complementary strategies for components that are crucial for the efficiency of CDCL, namely branching heuristics, learned constraint deletion and restarts. However, these strategies are mostly reused by PB solvers without considering the particular form of the PB constraints they deal with. In this paper, we present and evaluate different ways of adapting CDCL strategies to take the specificities of PB constraints into account while preserving the behavior they have in the clausal setting. We implemented these strategies in two different solvers, namely Sat4j (for which we consider three configurations) and RoundingSat. Our experiments show that these dedicated strategies allow to improve, sometimes significantly, the performance of these solvers, both on decision and optimization problems.
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