arXiv subjects

Youhei Akimoto

Publications and source records attributed to Youhei Akimoto.

At least 55 records · Page 3Linked to original sources

arXiv2022

A Two-phase Framework with a Bézier Simplex-based Interpolation Method for Computationally Expensive Multi-objective Optimization

This paper proposes a two-phase framework with a Bézier simplex-based interpolation method (TPB) for computationally expensive multi-objective optimization. The first phase in TPB aims to approximate a few Pareto optimal solutions by optimizing a sequence of single-objective scalar problems. The first phase in TPB can fully exploit a state-of-the-art single-objective derivative-free optimizer. The second phase in TPB utilizes a Bézier simplex model to interpolate the solutions obtained in the first phase. The second phase in TPB fully exploits the fact that a Bézier simplex model can approximate the Pareto optimal solution set by exploiting its simplex structure when a given problem is simplicial. We investigate the performance of TPB on the 55 bi-objective BBOB problems. The results show that TPB performs significantly better than HMO-CMA-ES and some state-of-the-art meta-model-based optimizers.

math.OC↗

arXiv2022

Global Linear Convergence of Evolution Strategies on More Than Smooth Strongly Convex Functions

Evolution strategies (ESs) are zeroth-order stochastic black-box optimization heuristics invariant to monotonic transformations of the objective function. They evolve a multivariate normal distribution, from which candidate solutions are generated. Among different variants, CMA-ES is nowadays recognized as one of the state-of-the-art zeroth-order optimizers for difficult problems. Albeit ample empirical evidence that ESs with a step-size control mechanism converge linearly, theoretical guarantees of linear convergence of ESs have been established only on limited classes of functions. In particular, theoretical results on convex functions are missing, where zeroth-order and also first-order optimization methods are often analyzed. In this paper, we establish almost sure linear convergence and a bound on the expected hitting time of an \new{ES family, namely the $(1+1)_κ$-ES, which includes the (1+1)-ES with (generalized) one-fifth success rule} and an abstract covariance matrix adaptation with bounded condition number, on a broad class of functions. The analysis holds for monotonic transformations of positively homogeneous functions and of quadratically bounded functions, the latter of which particularly includes monotonic transformation of strongly convex functions with Lipschitz continuous gradient. As far as the authors know, this is the first work that proves linear convergence of ES on such a broad class of functions.

math.NA↗

arXiv2022

Optimization on Planning of Trajectory and Control of Autonomous Berthing and Unberthing for the Realistic Port Geometry

To realize autonomous shipping, autonomous berthing and unberthing are some of the technical challenges. In the past, numerous research have been done on the optimization of trajectory planning of berthing problems. However, these studies assumed only a simple berth and did not consider obstacles. Optimization of trajectory planning on berthing and unberthing in actual ports must consider the spatial constraints and maintain sufficient distance to obstacles. The main contributions of this study are as follows: (i) a collision avoidance algorithm based on the ship domain which has variable size by the ship speed is proposed, to include the spatial constraints to optimization; (ii) the effect of wind disturbance is taken into account to the trajectory planning to make a feasible trajectory based on the capacity limit of actuators; (iii) showing that the optimization method for berthing is also eligible for the unberthing, which has been almost neglected; (iv) waypoints are included to the optimization process, to make optimization easier on practical applications. The authors tested the proposed method on two existing ports. The proposed method performed well on both the berthing and the unberthing problem and optimized the control input and the trajectory while avoiding collision with the complex obstacles.

math.OC↗

arXiv2022

Saddle Point Optimization with Approximate Minimization Oracle and its Application to Robust Berthing Control

We propose an approach to saddle point optimization relying only on oracles that solve minimization problems approximately. We analyze its convergence property on a strongly convex--concave problem and show its linear convergence toward the global min--max saddle point. Based on the convergence analysis, we develop a heuristic approach to adapt the learning rate. An implementation of the developed approach using the (1+1)-CMA-ES as the minimization oracle, namely Adversarial-CMA-ES, is shown to outperform several existing approaches on test problems. Numerical evaluation confirms the tightness of the theoretical convergence rate bound as well as the efficiency of the learning rate adaptation mechanism. As an example of real-world problems, the suggested optimization method is applied to automatic berthing control problems under model uncertainties, showing its usefulness in obtaining solutions robust to uncertainty.

math.OC↗

arXiv2021

An ODE Method to Prove the Geometric Convergence of Adaptive Stochastic Algorithms

We consider stochastic algorithms derived from methods for solving deterministic optimization problems, especially comparison-based algorithms derived from stochastic approximation algorithms with a constant step-size. We develop a methodology for proving geometric convergence of the parameter sequence $\{θ_n\}_{n\geq 0}$ of such algorithms. We employ the ordinary differential equation (ODE) method, which relates a stochastic algorithm to its mean ODE, along with a Lyapunov-like function $Ψ$ such that the geometric convergence of $Ψ(θ_n)$ implies -- in the case of an optimization algorithm -- the geometric convergence of the expected distance between the optimum and the search point generated by the algorithm. We provide two sufficient conditions for $Ψ(θ_n)$ to decrease at a geometric rate: $Ψ$ should decrease "exponentially" along the solution to the mean ODE, and the deviation between the stochastic algorithm and the ODE solution (measured by $Ψ$) should be bounded by $Ψ(θ_n)$ times a constant. We also provide practical conditions under which the two sufficient conditions may be verified easily without knowing the solution of the mean ODE. Our results are any-time bounds on $Ψ(θ_n)$, so we can deduce not only the asymptotic upper bound on the convergence rate, but also the first hitting time of the algorithm. The main results are applied to a comparison-based stochastic algorithm with a constant step-size for optimization on continuous domains.

math.OC↗

arXiv2021

System Parameter Exploration of Ship Maneuvering Model for Automatic Docking / Berthing using CMA-ES

Accurate maneuvering estimation is essential to establish autonomous berthing control. The system-based mathematical model is widely used to estimate the ship's maneuver. Commonly, the system parameters of the mathematical model are obtained by the captive model test (CMT), which is time-consuming to construct an accurate model suitable for complex berthing maneuvers. System identification (SI) is an alternative to constructing the mathematical model. However, SI on the mathematical model of ship's maneuver has been only conducted on much simpler maneuver: turning and zig-zag. Therefore, this study investigates the SI on a mathematical model capable of berthing maneuver. The main contributions of this study are as follows: (i) construct the system-based mathematical model on berthing by optimizing system parameters with a reduced amount of model tests than the CMT-based scheme; (ii) Find the favorable choice of objective function and type of training data for optimization. Global optimization scheme CMA-ES explored the system parameters of the MMG model from the free-running model's trajectories. The berthing simulation with the parameters obtained by the proposed method showed better agreement with the free-running model test than parameters obtained by the CMT. Furthermore, the proposed method required fewer data amounts than a CMT-based scheme.

eess.SY↗

arXiv2021

Unauthorized AI cannot Recognize Me: Reversible Adversarial Example

In this study, we propose a new methodology to control how user's data is recognized and used by AI via exploiting the properties of adversarial examples. For this purpose, we propose reversible adversarial example (RAE), a new type of adversarial example. A remarkable feature of RAE is that the image can be correctly recognized and used by the AI model specified by the user because the authorized AI can recover the original image from the RAE exactly by eliminating adversarial perturbation. On the other hand, other unauthorized AI models cannot recognize it correctly because it functions as an adversarial example. Moreover, RAE can be considered as one type of encryption to computer vision since reversibility guarantees the decryption. To realize RAE, we combine three technologies, adversarial example, reversible data hiding for exact recovery of adversarial perturbation, and encryption for selective control of AIs who can remove adversarial perturbation. Experimental results show that the proposed method can achieve comparable attack ability with the corresponding adversarial attack method and similar visual quality with the original image, including white-box attacks and black-box attacks.

cs.CV↗

arXiv2021

Unsupervised Causal Binary Concepts Discovery with VAE for Black-box Model Explanation

We aim to explain a black-box classifier with the form: `data X is classified as class Y because X \textit{has} A, B and \textit{does not have} C' in which A, B, and C are high-level concepts. The challenge is that we have to discover in an unsupervised manner a set of concepts, i.e., A, B and C, that is useful for the explaining the classifier. We first introduce a structural generative model that is suitable to express and discover such concepts. We then propose a learning process that simultaneously learns the data distribution and encourages certain concepts to have a large causal influence on the classifier output. Our method also allows easy integration of user's prior knowledge to induce high interpretability of concepts. Using multiple datasets, we demonstrate that our method can discover useful binary concepts for explanation.

cs.LG↗

arXiv2021

Level Generation for Angry Birds with Sequential VAE and Latent Variable Evolution

Video game level generation based on machine learning (ML), in particular, deep generative models, has attracted attention as a technique to automate level generation. However, applications of existing ML-based level generations are mostly limited to tile-based level representation. When ML techniques are applied to game domains with non-tile-based level representation, such as Angry Birds, where objects in a level are specified by real-valued parameters, ML often fails to generate playable levels. In this study, we develop a deep-generative-model-based level generation for the game domain of Angry Birds. To overcome these drawbacks, we propose a sequential encoding of a level and process it as text data, whereas existing approaches employ a tile-based encoding and process it as an image. Experiments show that the proposed level generator drastically improves the stability and diversity of generated levels compared with existing approaches. We apply latent variable evolution with the proposed generator to control the feature of a generated level computed through an AI agent's play, while keeping the level stable and natural.

cs.AI↗

arXiv2021

Convergence Rate of the (1+1)-Evolution Strategy with Success-Based Step-Size Adaptation on Convex Quadratic Functions

The (1+1)-evolution strategy (ES) with success-based step-size adaptation is analyzed on a general convex quadratic function and its monotone transformation, that is, $f(x) = g((x - x^*)^\mathrm{T} H (x - x^*))$, where $g:\mathbb{R}\to\mathbb{R}$ is a strictly increasing function, $H$ is a positive-definite symmetric matrix, and $x^* \in \mathbb{R}^d$ is the optimal solution of $f$. The convergence rate, that is, the decrease rate of the distance from a search point $m_t$ to the optimal solution $x^*$, is proven to be in $O(\exp( - L / \mathrm{Tr}(H) ))$, where $L$ is the smallest eigenvalue of $H$ and $\mathrm{Tr}(H)$ is the trace of $H$. This result generalizes the known rate of $O(\exp(- 1/d ))$ for the case of $H = I_{d}$ ($I_d$ is the identity matrix of dimension $d$) and $O(\exp(- 1/ (d\cdotξ) ))$ for the case of $H = \mathrm{diag}(ξ\cdot I_{d/2}, I_{d/2})$. To the best of our knowledge, this is the first study in which the convergence rate of the (1+1)-ES is derived explicitly and rigorously on a general convex quadratic function, which depicts the impact of the distribution of the eigenvalues in the Hessian $H$ on the optimization and not only the impact of the condition number of $H$.

cs.NE↗

arXiv2021

Saddle Point Optimization with Approximate Minimization Oracle

A major approach to saddle point optimization $\min_x\max_y f(x, y)$ is a gradient based approach as is popularized by generative adversarial networks (GANs). In contrast, we analyze an alternative approach relying only on an oracle that solves a minimization problem approximately. Our approach locates approximate solutions $x'$ and $y'$ to $\min_{x'}f(x', y)$ and $\max_{y'}f(x, y')$ at a given point $(x, y)$ and updates $(x, y)$ toward these approximate solutions $(x', y')$ with a learning rate $η$. On locally strong convex--concave smooth functions, we derive conditions on $η$ to exhibit linear convergence to a local saddle point, which reveals a possible shortcoming of recently developed robust adversarial reinforcement learning algorithms. We develop a heuristic approach to adapt $η$ derivative-free and implement zero-order and first-order minimization algorithms. Numerical experiments are conducted to show the tightness of the theoretical results as well as the usefulness of the $η$ adaptation mechanism.

math.OC↗

arXiv2021

AdvantageNAS: Efficient Neural Architecture Search with Credit Assignment

Neural architecture search (NAS) is an approach for automatically designing a neural network architecture without human effort or expert knowledge. However, the high computational cost of NAS limits its use in commercial applications. Two recent NAS paradigms, namely one-shot and sparse propagation, which reduce the time and space complexities, respectively, provide clues for solving this problem. In this paper, we propose a novel search strategy for one-shot and sparse propagation NAS, namely AdvantageNAS, which further reduces the time complexity of NAS by reducing the number of search iterations. AdvantageNAS is a gradient-based approach that improves the search efficiency by introducing credit assignment in gradient estimation for architecture updates. Experiments on the NAS-Bench-201 and PTB dataset show that AdvantageNAS discovers an architecture with higher performance under a limited time budget compared to existing sparse propagation NAS. To further reveal the reliabilities of AdvantageNAS, we investigate it theoretically and find that it monotonically improves the expected loss and thus converges.

cs.LG↗

arXiv2020

Warm Starting CMA-ES for Hyperparameter Optimization

Hyperparameter optimization (HPO), formulated as black-box optimization (BBO), is recognized as essential for automation and high performance of machine learning approaches. The CMA-ES is a promising BBO approach with a high degree of parallelism, and has been applied to HPO tasks, often under parallel implementation, and shown superior performance to other approaches including Bayesian optimization (BO). However, if the budget of hyperparameter evaluations is severely limited, which is often the case for end users who do not deserve parallel computing, the CMA-ES exhausts the budget without improving the performance due to its long adaptation phase, resulting in being outperformed by BO approaches. To address this issue, we propose to transfer prior knowledge on similar HPO tasks through the initialization of the CMA-ES, leading to significantly shortening the adaptation time. The knowledge transfer is designed based on the novel definition of task similarity, with which the correlation of the performance of the proposed approach is confirmed on synthetic problems. The proposed warm starting CMA-ES, called WS-CMA-ES, is applied to different HPO tasks where some prior knowledge is available, showing its superior performance over the original CMA-ES as well as BO approaches with or without using the prior knowledge.

cs.LG↗

arXiv2020

Statistically Significant Pattern Mining with Ordinal Utility

Statistically significant patterns mining (SSPM) is an essential and challenging data mining task in the field of knowledge discovery in databases (KDD), in which each pattern is evaluated via a hypothesis test. Our study aims to introduce a preference relation into patterns and to discover the most preferred patterns under the constraint of statistical significance, which has never been considered in existing SSPM problems. We propose an iterative multiple testing procedure that can alternately reject a hypothesis and safely ignore the hypotheses that are less useful than the rejected hypothesis. One advantage of filtering out patterns with low utility is that it avoids consumption of the significance budget by rejection of useless (that is, uninteresting) patterns. This allows the significance budget to be focused on useful patterns, leading to more useful discoveries. We show that the proposed method can control the familywise error rate (FWER) under certain assumptions, that can be satisfied by a realistic problem class in SSPM.\@We also show that the proposed method always discovers a set of patterns that is at least equally or more useful than those discovered using the standard Tarone-Bonferroni method SSPM.\@Finally, we conducted several experiments with both synthetic and real-world data to evaluate the performance of our method. As a result, in the experiments with real-world datasets, the proposed method discovered a larger number of more useful patterns than the existing method for all five conducted tasks.

stat.ME↗

arXiv2019

Generate (non-software) Bugs to Fool Classifiers

In adversarial attacks intended to confound deep learning models, most studies have focused on limiting the magnitude of the modification so that humans do not notice the attack. On the other hand, during an attack against autonomous cars, for example, most drivers would not find it strange if a small insect image were placed on a stop sign, or they may overlook it. In this paper, we present a systematic approach to generate natural adversarial examples against classification models by employing such natural-appearing perturbations that imitate a certain object or signal. We first show the feasibility of this approach in an attack against an image classifier by employing generative adversarial networks that produce image patches that have the appearance of a natural object to fool the target model. We also introduce an algorithm to optimize placement of the perturbation in accordance with the input image, which makes the generation of adversarial examples fast and likely to succeed. Moreover, we experimentally show that the proposed approach can be extended to the audio domain, for example, to generate perturbations that sound like the chirping of birds to fool a speech classifier.

cs.LG↗

arXiv2019

Adaptive Stochastic Natural Gradient Method for One-Shot Neural Architecture Search

High sensitivity of neural architecture search (NAS) methods against their input such as step-size (i.e., learning rate) and search space prevents practitioners from applying them out-of-the-box to their own problems, albeit its purpose is to automate a part of tuning process. Aiming at a fast, robust, and widely-applicable NAS, we develop a generic optimization framework for NAS. We turn a coupled optimization of connection weights and neural architecture into a differentiable optimization by means of stochastic relaxation. It accepts arbitrary search space (widely-applicable) and enables to employ a gradient-based simultaneous optimization of weights and architecture (fast). We propose a stochastic natural gradient method with an adaptive step-size mechanism built upon our theoretical investigation (robust). Despite its simplicity and no problem-dependent parameter tuning, our method exhibited near state-of-the-art performances with low computational budgets both on image classification and inpainting tasks.

cs.LG↗

arXiv2019

Diagonal Acceleration for Covariance Matrix Adaptation Evolution Strategies

We introduce an acceleration for covariance matrix adaptation evolution strategies (CMA-ES) by means of adaptive diagonal decoding (dd-CMA). This diagonal acceleration endows the default CMA-ES with the advantages of separable CMA-ES without inheriting its drawbacks. Technically, we introduce a diagonal matrix D that expresses coordinate-wise variances of the sampling distribution in DCD form. The diagonal matrix can learn a rescaling of the problem in the coordinates within linear number of function evaluations. Diagonal decoding can also exploit separability of the problem, but, crucially, does not compromise the performance on non-separable problems. The latter is accomplished by modulating the learning rate for the diagonal matrix based on the condition number of the underlying correlation matrix. dd-CMA-ES not only combines the advantages of default and separable CMA-ES, but may achieve overadditive speedup: it improves the performance, and even the scaling, of the better of default and separable CMA-ES on classes of non-separable test functions that reflect, arguably, a landscape feature commonly observed in practice. The paper makes two further secondary contributions: we introduce two different approaches to guarantee positive definiteness of the covariance matrix with active CMA, which is valuable in particular with large population size; we revise the default parameter setting in CMA-ES, proposing accelerated settings in particular for large dimension. All our contributions can be viewed as independent improvements of CMA-ES, yet they are also complementary and can be seamlessly combined. In numerical experiments with dd-CMA-ES up to dimension 5120, we observe remarkable improvements over the original covariance matrix adaptation on functions with coordinate-wise ill-conditioning. The improvement is observed also for large population sizes up to about dimension squared.

cs.NE↗

arXiv2019

Drift Theory in Continuous Search Spaces: Expected Hitting Time of the (1+1)-ES with 1/5 Success Rule

This paper explores the use of the standard approach for proving runtime bounds in discrete domains---often referred to as drift analysis---in the context of optimization on a continuous domain. Using this framework we analyze the (1+1) Evolution Strategy with one-fifth success rule on the sphere function. To deal with potential functions that are not lower-bounded, we formulate novel drift theorems. We then use the theorems to prove bounds on the expected hitting time to reach a certain target fitness in finite dimension $d$. The bounds are akin to linear convergence. We then study the dependency of the different terms on $d$ proving a convergence rate dependency of $Θ(1/d)$. Our results constitute the first non-asymptotic analysis for the algorithm considered as well as the first explicit application of drift analysis to a randomized search heuristic with continuous domain.

cs.NE↗