arXiv subjects

So Nakashima

Publications and source records attributed to So Nakashima.

9 recordsLinked to original sources

arXiv2026

Accelerating Evolutionary Strategy via Rao-Blackwellizing Realization of Uncertain Input

We investigate Optimization under Input Uncertainty (OIU), in which the input to the objective function, rather than the objective function itself, is subject to uncertainty. OIU appears in manufacturing processes with production tolerance, control of physical systems with actuation noise, Mixture of Experts, and Reinforcement Learning (RL). Most of the existing approaches solve OIU by using the value of the objective function but discard the information of the realized input, even though the realized input is observable in various applications. The question here is whether the discarded information of the realized input is useful to accelerate the optimization process. We affirmatively answer this question for Evolutionary Strategy (ES) by theoretically showing that the information of the realized input can reduce the variance of the gradient estimator via Rao-Blackwellization. Using the Rao-Blackwellized gradient estimator, we propose Phenotype-Accelerated Evolutionary Strategy (PAES), which is a refinement of ES for OIU. Numerical experiments show that PAES converges faster than the usual ES from simple continuous optimization problems to RL benchmarks.

math.OC↗

arXiv2024

Ancestral Reinforcement Learning: Unifying Zeroth-Order Optimization and Genetic Algorithms for Reinforcement Learning

Reinforcement Learning (RL) offers a fundamental framework for discovering optimal action strategies through interactions within unknown environments. Recent advancement have shown that the performance and applicability of RL can significantly be enhanced by exploiting a population of agents in various ways. Zeroth-Order Optimization (ZOO) leverages an agent population to estimate the gradient of the objective function, enabling robust policy refinement even in non-differentiable scenarios. As another application, Genetic Algorithms (GA) boosts the exploration of policy landscapes by mutational generation of policy diversity in an agent population and its refinement by selection. A natural question is whether we can have the best of two worlds that the agent population can have. In this work, we propose Ancestral Reinforcement Learning (ARL), which synergistically combines the robust gradient estimation of ZOO with the exploratory power of GA. The key idea in ARL is that each agent within a population infers gradient by exploiting the history of its ancestors, i.e., the ancestor population in the past, while maintaining the diversity of policies in the current population as in GA. We also theoretically reveal that the populational search in ARL implicitly induces the KL-regularization of the objective function, resulting in the enhanced exploration. Our results extend the applicability of populational algorithms for RL.

cs.LG↗

arXiv2021

Acceleration of Evolutionary Processes by Learning and Extended Fisher's Fundamental Theorem

Natural selection is general and powerful concept not only to explain evolutionary processes of biological organisms but also to design engineering systems such as genetic algorithms and particle filters. There is a surge of interest, both from biology and engineering, in considering natural selection of intellectual agents that can learn individually. Learning by individual agents of better behaviors for survival may accelerate the evolutionary processes by natural selection. We have accumulating pieces of evidence that organisms can transmit its information to the next generation via epigenetic states or memes. Also, such idea is important for engineering applications. To accelerate the evolutionary process, an agent should change their strategy so that the population fitness increases the most. Equivalently, an agent should update the strategy towards a gradient of the population fitness. However, it has not yet been clarified whether and how an agent can estimate the gradient and accelerate the evolutionary process. We also lack methodology to quantify the acceleration to understand and predict the impact of learning. In this paper, we address these problems. We show that an learning agent can accelerate the evolutionary process by proposing ancestral learning, which uses the information transmitted from the ancestor (ancestral information). We next show that the ancestral information is sufficient to estimate the gradient. In particular, learning can accelerate the evolutionary process without communications between agents. Finally, to quantify the acceleration, we extend the Fisher's fundamental theorem (FF-thm) for natural selection to ancestral learning. Our extended FF-thm relates the acceleration of the evolutionary process to the variety of individual fitness of the agent. By the theorem, we can quantitatively understand when and why learning is beneficial.

q-bio.PE↗

arXiv2020

Rank axiom of modular supermatroids: A connection with directional DR submodular functions

A matroid has been one of the most important combinatorial structures since it was introduced by Whitney as an abstraction of linear independence. As an important property of a matroid, it can be characterized by several different (but equivalent) axioms, such as the augmentation, the base exchange, or the rank axiom. A supermatroid is a generalization of a matroid defined on lattices. Here, the central question is whether a supermatroid can be characterized by several equivalent axioms similar to a matroid. Barnabei, Nicoletti, and Pezzoli characterized supermatroids on distributive lattices, and Fujishige, Koshevoy, and Sano generalized the results for cg-matroids (supermatroids on lower locally distributive lattices). In this study, we focus on modular lattices, which are an important superclass of distributive lattices, and provide equivalent characterizations of supermatroids on modular lattices. We characterize supermatroids on modular lattices using the rank axiom in which the rank function is a directional DR-submodular function, which is a generalization of a submodular function introduced by the authors. Using a characterization based on rank functions, we further prove the strong exchange property of a supermatroid, which has application in optimization. We also reveal the relation between the axioms of a supermatroid on lower semimodular lattices, which is a common superclass of a lower locally distributive lattice and a modular lattice.

math.CO↗

arXiv2019

Lineage EM Algorithm for Inferring Latent States from Cellular Lineage Trees

Phenotypic variability in a population of cells can work as the bet-hedging of the cells under an unpredictably changing environment, the typical example of which is the bacterial persistence. To understand the strategy to control such phenomena, it is indispensable to identify the phenotype of each cell and its inheritance. Although recent advancements in microfluidic technology offer us useful lineage data, they are insufficient to directly identify the phenotypes of the cells. An alternative approach is to infer the phenotype from the lineage data by latent-variable estimation. To this end, however, we must resolve the bias problem in the inference from lineage called survivorship bias. In this work, we clarify how the survivor bias distorts statistical estimations. We then propose a latent-variable estimation algorithm without the survivorship bias from lineage trees based on an expectation-maximization (EM) algorithm, which we call Lineage EM algorithm (LEM). LEM provides a statistical method to identify the traits of the cells applicable to various kinds of lineage data.

q-bio.PE↗

arXiv2019

Multiple Knapsack-Constrained Monotone DR-Submodular Maximization on Distributive Lattice --- Continuous Greedy Algorithm on Median Complex ---

We consider a problem of maximizing a monotone DR-submodular function under multiple order-consistent knapsack constraints on a distributive lattice. Since a distributive lattice is used to represent a dependency constraint, the problem can represent a dependency constrained version of a submodular maximization problem on a set. We propose a $1 - 1/e$ approximation algorithm for this problem. To achieve this result, we generalize the continuous greedy algorithm to distributive lattices: We choose a median complex as a continuous relaxation of a distributive lattice and define the multilinear extension on it. We show that the median complex admits special curves, named uniform linear motions, such that the multilinear extension of a DR-submodular function is concave along a positive uniform linear motion, which is a key property of the continuous greedy algorithm.

cs.DS↗

arXiv2018

Fitness response relation of a multi-type age-structured population dynamics

We construct a pathwise formulation for a multi-type age-structured population dynamics, which involves an age-dependent cell replication and transition of gene- or phenotypes. By employing the formulation, we derive a variational representation of the stationary population growth rate; the representation comprises a trade-off relation between growth effects and a single-cell intrinsic dynamics described by a semi-Markov process. This variational representation leads to a response relation of the stationary population growth rate, in which statistics on a retrospective history work as the response coefficients. These results contribute to predicting and controlling growing populations based on experimentally observed cell-lineage information.

cond-mat.stat-mech↗

arXiv2018

Subspace Selection via DR-Submodular Maximization on Lattices

The subspace selection problem seeks a subspace that maximizes an objective function under some constraint. This problem includes several important machine learning problems such as the principal component analysis and sparse dictionary selection problem. Often, these problems can be solved by greedy algorithms. Here, we are interested in why these problems can be solved by greedy algorithms, and what classes of objective functions and constraints admit this property. To answer this question, we formulate the problems as optimization problems on lattices. Then, we introduce a new class of functions, directional DR-submodular functions, to characterize the approximability of problems. We see that the principal component analysis, sparse dictionary selection problem, and these generalizations have directional DR-submodularities. We show that, under several constraints, the directional DR-submodular function maximization problem can be solved efficiently with provable approximation factors.

cs.DS↗

arXiv2017

A Compact Representation for Modular Semilattices and its Applications

A modular semilattice is a semilattice generalization of a modular lattice. We establish a Birkhoff-type representation theorem for modular semilattices, which says that every modular semilattice is isomorphic to the family of ideals in a certain poset with additional relations.This new poset structure, which we axiomatize in this paper, is called a PPIP (projective poset with inconsistent pairs). A PPIP is a common generalization of a PIP (poset with inconsistent pairs) and a projective ordered space. The former was introduced by Barthélemy and Constantin for establishing Birkhoff-type theorem for median semilattices, and the latter by Herrmann, Pickering, and Roddy for modular lattices. We show the $Θ(n)$ representation complexityand a construction algorithm for PPIP-representations of $(\wedge, \vee)$-closed sets in the product $L^n$ of modular semilattice $L$. This generalizes the results of Hirai and Oki for a special median semilattice $S_k$. We also investigate implicational bases for modular semilattices. Extending earlier results of Wild and Herrmann for modular lattices, we determine optimal implicational bases and develop a polynomial time recognition algorithm for modular semilattices. These results can be applied to retain the minimizer set of a submodular function on a modular semilattice.

math.CO↗