CMA-ES with Learning Rate Adaptation

The covariance matrix adaptation evolution strategy (CMA-ES) is one of the most successful methods for solving continuous black-box optimization problems. A practically useful aspect of the CMA-ES is that it can be used without hyperparameter tuning. However, the hyperparameter settings still have a considerable impact on performance, especially for difficult tasks, such as solving multimodal or noisy problems. This study comprehensively explores the impact of learning rate on the CMA-ES performance and demonstrates the necessity of a small learning rate by considering ordinary differential equations. Thereafter, it discusses the setting of an ideal learning rate. Based on these discussions, we develop a novel learning rate adaptation mechanism for the CMA-ES that maintains a constant signal-to-noise ratio. Additionally, we investigate the behavior of the CMA-ES with the proposed learning rate adaptation mechanism through numerical experiments, and compare the results with those obtained for the CMA-ES with a fixed learning rate and with population size adaptation. The results show that the CMA-ES with the proposed learning rate adaptation works well for multimodal and/or noisy problems without extremely expensive learning rate tuning.

Theoretical Analysis of Explicit Averaging and Novel Sign Averaging in Comparison-Based Search

In black-box optimization, noise in the objective function is inevitable. Noise disrupts the ranking of candidate solutions in comparison-based optimization, possibly deteriorating the search performance compared with a noiseless scenario. Explicit averaging takes the sample average of noisy objective function values and is widely used as a simple and versatile noise-handling technique. Although it is suitable for various applications, it is ineffective if the mean is not finite. We theoretically reveal that explicit averaging has a negative effect on the estimation of ground-truth rankings when assuming stably distributed noise without a finite mean. Alternatively, sign averaging is proposed as a simple but robust noise-handling technique. We theoretically prove that the sign averaging estimates the order of the medians of the noisy objective function values of a pair of points with arbitrarily high probability as the number of samples increases. Its advantages over explicit averaging and its robustness are also confirmed through numerical experiments.

Verbosity Bias in Preference Labeling by Large Language Models

In recent years, Large Language Models (LLMs) have witnessed a remarkable surge in prevalence, altering the landscape of natural language processing and machine learning. One key factor in improving the performance of LLMs is alignment with humans achieved with Reinforcement Learning from Human Feedback (RLHF), as for many LLMs such as GPT-4, Bard, etc. In addition, recent studies are investigating the replacement of human feedback with feedback from other LLMs named Reinforcement Learning from AI Feedback (RLAIF). We examine the biases that come along with evaluating LLMs with other LLMs and take a closer look into verbosity bias -- a bias where LLMs sometimes prefer more verbose answers even if they have similar qualities. We see that in our problem setting, GPT-4 prefers longer answers more than humans. We also propose a metric to measure this bias.

Statistically Significant Concept-based Explanation of Image Classifiers via Model Knockoffs

A concept-based classifier can explain the decision process of a deep learning model by human-understandable concepts in image classification problems. However, sometimes concept-based explanations may cause false positives, which misregards unrelated concepts as important for the prediction task. Our goal is to find the statistically significant concept for classification to prevent misinterpretation. In this study, we propose a method using a deep learning model to learn the image concept and then using the Knockoff samples to select the important concepts for prediction by controlling the False Discovery Rate (FDR) under a certain value. We evaluate the proposed method in our synthetic and real data experiments. Also, it shows that our method can control the FDR properly while selecting highly interpretable concepts to improve the trustworthiness of the model.

CMA-ES with Learning Rate Adaptation: Can CMA-ES with Default Population Size Solve Multimodal and Noisy Problems?

The covariance matrix adaptation evolution strategy (CMA-ES) is one of the most successful methods for solving black-box continuous optimization problems. One practically useful aspect of the CMA-ES is that it can be used without hyperparameter tuning. However, the hyperparameter settings still have a considerable impact, especially for difficult tasks such as solving multimodal or noisy problems. In this study, we investigate whether the CMA-ES with default population size can solve multimodal and noisy problems. To perform this investigation, we develop a novel learning rate adaptation mechanism for the CMA-ES, such that the learning rate is adapted so as to maintain a constant signal-to-noise ratio. We investigate the behavior of the CMA-ES with the proposed learning rate adaptation mechanism through numerical experiments, and compare the results with those obtained for the CMA-ES with a fixed learning rate. The results demonstrate that, when the proposed learning rate adaptation is used, the CMA-ES with default population size works well on multimodal and/or noisy problems, without the need for extremely expensive learning rate tuning.

Covariance Matrix Adaptation Evolutionary Strategy with Worst-Case Ranking Approximation for Min--Max Optimization and its Application to Berthing Control Tasks

In this study, we consider a continuous min--max optimization problem $\min_{x \in \mathbb{X} \max_{y \in \mathbb{Y}}}f(x,y)$ whose objective function is a black-box. We propose a novel approach to minimize the worst-case objective function $F(x) = \max_{y} f(x,y)$ directly using a covariance matrix adaptation evolution strategy (CMA-ES) in which the rankings of solution candidates are approximated by our proposed worst-case ranking approximation (WRA) mechanism. We develop two variants of WRA combined with CMA-ES and approximate gradient ascent as numerical solvers for the inner maximization problem. Numerical experiments show that our proposed approach outperforms several existing approaches when the objective function is a smooth strongly convex--concave function and the interaction between $x$ and $y$ is strong. We investigate the advantages of the proposed approach for problems where the objective function is not limited to smooth strongly convex--concave functions. The effectiveness of the proposed approach is demonstrated in the robust berthing control problem with uncertainty.ngly convex--concave functions. The effectiveness of the proposed approach is demonstrated in the robust berthing control problem with uncertainty.

Few-Shot Image-to-Semantics Translation for Policy Transfer in Reinforcement Learning

We investigate policy transfer using image-to-semantics translation to mitigate learning difficulties in vision-based robotics control agents. This problem assumes two environments: a simulator environment with semantics, that is, low-dimensional and essential information, as the state space, and a real-world environment with images as the state space. By learning mapping from images to semantics, we can transfer a policy, pre-trained in the simulator, to the real world, thereby eliminating real-world on-policy agent interactions to learn, which are costly and risky. In addition, using image-to-semantics mapping is advantageous in terms of the computational efficiency to train the policy and the interpretability of the obtained policy over other types of sim-to-real transfer strategies. To tackle the main difficulty in learning image-to-semantics mapping, namely the human annotation cost for producing a training dataset, we propose two techniques: pair augmentation with the transition function in the simulator environment and active learning. We observed a reduction in the annotation cost without a decline in the performance of the transfer, and the proposed approach outperformed the existing approach without annotation.

Collision probability reduction method for tracking control in automatic docking / berthing using reinforcement learning

Automation of berthing maneuvers in shipping is a pressing issue as the berthing maneuver is one of the most stressful tasks seafarers undertake. Berthing control problems are often tackled via tracking a predefined trajectory or path. Maintaining a tracking error of zero under an uncertain environment is impossible; the tracking controller is nonetheless required to bring vessels close to desired berths. The tracking controller must prioritize the avoidance of tracking errors that may cause collisions with obstacles. This paper proposes a training method based on reinforcement learning for a trajectory tracking controller that reduces the probability of collisions with static obstacles. Via numerical simulations, we show that the proposed method reduces the probability of collisions during berthing maneuvers. Furthermore, this paper shows the tracking performance in a model experiment.

Adaptive Scenario Subset Selection for Worst-Case Optimization and its Application to Well Placement Optimization

In this study, we consider simulation-based worst-case optimization problems with continuous design variables and a finite scenario set. To reduce the number of simulations required and increase the number of restarts for better local optimum solutions, we propose a new approach referred to as adaptive scenario subset selection (AS3). The proposed approach subsamples a scenario subset as a support to construct the worst-case function in a given neighborhood, and we introduce such a scenario subset. Moreover, we develop a new optimization algorithm by combining AS3 and the covariance matrix adaptation evolution strategy (CMA-ES), denoted AS3-CMA-ES. At each algorithmic iteration, a subset of support scenarios is selected, and CMA-ES attempts to optimize the worst-case objective computed only through a subset of the scenarios. The proposed algorithm reduces the number of simulations required by executing simulations on only a scenario subset, rather than on all scenarios. In numerical experiments, we verified that AS3-CMA-ES is more efficient in terms of the number of simulations than the brute-force approach and a surrogate-assisted approach lq-CMA-ES when the ratio of the number of support scenarios to the total number of scenarios is relatively small. In addition, the usefulness of AS3-CMA-ES was evaluated for well placement optimization for carbon dioxide capture and storage (CCS). In comparison with the brute-force approach and lq-CMA-ES, AS3-CMA-ES was able to find better solutions because of more frequent restarts.