arXiv subjects

Yuichi Yoshida

Publications and source records attributed to Yuichi Yoshida.

At least 37 records · Page 2Linked to original sources

arXiv2025

Sensitivity Lower Bounds for Approximaiton Algorithms

Sensitivity measures how much the output of an algorithm changes, in terms of Hamming distance, when part of the input is modified. While approximation algorithms with low sensitivity have been developed for many problems, no sensitivity lower bounds were previously known for approximation algorithms. In this work, we establish the first polynomial lower bound on the sensitivity of (randomized) approximation algorithms for constraint satisfaction problems (CSPs) by adapting the probabilistically checkable proof (PCP) framework to preserve sensitivity lower bounds. From this, we derive polynomial sensitivity lower bounds for approximation algorithms for a variety of problems, including maximum clique, minimum vertex cover, and maximum cut. Leveraging the connection between sensitivity and locality in the non-signaling model, which subsumes the LOCAL, quantum-LOCAL, and bounded dependence models, we establish locality lower bounds for several graph problems in the non-signaling model.

cs.DS↗

arXiv2025

From Generative to Episodic: Sample-Efficient Replicable Reinforcement Learning

The epidemic failure of replicability across empirical science and machine learning has recently motivated the formal study of replicable learning algorithms [Impagliazzo et al. (2022)]. In batch settings where data comes from a fixed i.i.d. source (e.g., hypothesis testing, supervised learning), the design of data-efficient replicable algorithms is now more or less understood. In contrast, there remain significant gaps in our knowledge for control settings like reinforcement learning where an agent must interact directly with a shifting environment. Karbasi et. al show that with access to a generative model of an environment with $S$ states and $A$ actions (the RL 'batch setting'), replicably learning a near-optimal policy costs only $\tilde{O}(S^2A^2)$ samples. On the other hand, the best upper bound without a generative model jumps to $\tilde{O}(S^7 A^7)$ [Eaton et al. (2024)] due to the substantial difficulty of environment exploration. This gap raises a key question in the broader theory of replicability: Is replicable exploration inherently more expensive than batch learning? Is sample-efficient replicable RL even possible? In this work, we (nearly) resolve this problem (for low-horizon tabular MDPs): exploration is not a significant barrier to replicable learning! Our main result is a replicable RL algorithm on $\tilde{O}(S^2A)$ samples, bridging the gap between the generative and episodic settings. We complement this with a matching $\tildeΩ(S^2A)$ lower bound in the generative setting (under the common parallel sampling assumption) and an unconditional lower bound in the episodic setting of $\tildeΩ(S^2)$ showcasing the near-optimality of our algorithm with respect to the state space $S$.

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arXiv2025

Courcelle's Theorem for Lipschitz Continuity

Lipschitz continuity of algorithms, introduced by Kumabe and Yoshida (FOCS'23), measures the stability of an algorithm against small input perturbations. Algorithms with small Lipschitz continuity are desirable, as they ensure reliable decision-making and reproducible scientific research. Several studies have proposed Lipschitz continuous algorithms for various combinatorial optimization problems, but these algorithms are problem-specific, requiring a separate design for each problem. To address this issue, we provide the first algorithmic meta-theorem in the field of Lipschitz continuous algorithms. Our result can be seen as a Lipschitz continuous analogue of Courcelle's theorem, which offers Lipschitz continuous algorithms for problems on bounded-treewidth graphs. Specifically, we consider the problem of finding a vertex set in a graph that maximizes or minimizes the total weight, subject to constraints expressed in monadic second-order logic (MSO_2). We show that for any $\varepsilon>0$, there exists a $(1\pm \varepsilon)$-approximation algorithm for the problem with a polylogarithmic Lipschitz constant on bounded treewidth graphs. On such graphs, our result outperforms most existing Lipschitz continuous algorithms in terms of approximability and/or Lipschitz continuity. Further, we provide similar results for problems on bounded-clique-width graphs subject to constraints expressed in MSO_1. Additionally, we construct a Lipschitz continuous version of Baker's decomposition using our meta-theorem as a subroutine.

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arXiv2025

The minimum number of vertices and edges of connected graphs with ind-match$(G) = p$, min-match$(G) = q$ and match$(G) = r$

Let ind-match$(G)$, min-match$(G)$ and match$(G)$ denote the induced matching number, minimum matching number and matching number of a graph $G$, respectively. It is known that ind-match$(G) \leq $ min-match$(G) \leq {\rm match}(G) \leq$ 2min-match$(G)$ holds. In the present paper, we investigate the minimum number of vertices and edges of connencted simple graphs $G$ with ind-match$(G) = p$, min-match$(G) = q$ and ${\rm match}(G) = r$ for pair of integers $p, q, r$ such that $1 \leq p \leq q \leq r \leq 2q$.

math.CO↗

arXiv2024

Lipschitz Continuous Algorithms for Covering Problems

Combinatorial algorithms are widely used for decision-making and knowledge discovery, and it is important to ensure that their output remains stable even when subjected to small perturbations in the input. Failure to do so can lead to several problems, including costly decisions, reduced user trust, potential security concerns, and lack of replicability. Unfortunately, many fundamental combinatorial algorithms are vulnerable to small input perturbations. To address the impact of input perturbations on algorithms for weighted graph problems, Kumabe and Yoshida (FOCS'23) recently introduced the concept of Lipschitz continuity of algorithms. This work explores this approach and designs Lipschitz continuous algorithms for covering problems, such as the minimum vertex cover, set cover, and feedback vertex set problems. Our algorithm for the feedback vertex set problem is based on linear programming, and in the rounding process, we develop and use a technique called cycle sparsification, which may be of independent interest.

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arXiv2024

Stochastic Distance in Property Testing

We introduce a novel concept termed "stochastic distance" for property testing. Diverging from the traditional definition of distance, where a distance $t$ implies that there exist $t$ edges that can be added to ensure a graph possesses a certain property (such as $k$-edge-connectivity), our new notion implies that there is a high probability that adding $t$ random edges will endow the graph with the desired property. While formulating testers based on this new distance proves challenging in a sequential environment, it is much easier in a distributed setting. Taking $k$-edge-connectivity as a case study, we design ultra-fast testing algorithms in the CONGEST model. Our introduction of stochastic distance offers a more natural fit for the distributed setting, providing a promising avenue for future research in emerging models of computation.

cs.DC↗

arXiv2024

Average sensitivity of the Knapsack Problem

In resource allocation, we often require that the output allocation of an algorithm is stable against input perturbation because frequent reallocation is costly and untrustworthy. Varma and Yoshida (SODA'21) formalized this requirement for algorithms as the notion of average sensitivity. Here, the average sensitivity of an algorithm on an input instance is, roughly speaking, the average size of the symmetric difference of the output for the instance and that for the instance with one item deleted, where the average is taken over the deleted item. In this work, we consider the average sensitivity of the knapsack problem, a representative example of a resource allocation problem. We first show a $(1-ε)$-approximation algorithm for the knapsack problem with average sensitivity $O(ε^{-1}\log ε^{-1})$. Then, we complement this result by showing that any $(1-ε)$-approximation algorithm has average sensitivity $Ω(ε^{-1})$. As an application of our algorithm, we consider the incremental knapsack problem in the random-order setting, where the goal is to maintain a good solution while items arrive one by one in a random order. Specifically, we show that for any $ε> 0$, there exists a $(1-ε)$-approximation algorithm with amortized recourse $O(ε^{-1}\log ε^{-1})$ and amortized update time $O(\log n+f_ε)$, where $n$ is the total number of items and $f_ε>0$ is a value depending on $ε$.

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arXiv2024

Lipschitz Continuous Allocations for Optimization Games

In cooperative game theory, the primary focus is the equitable allocation of payoffs or costs among agents. However, in the practical applications of cooperative games, accurately representing games is challenging. In such cases, using an allocation method sensitive to small perturbations in the game can lead to various problems, including dissatisfaction among agents and the potential for manipulation by agents seeking to maximize their own benefits. Therefore, the allocation method must be robust against game perturbations. In this study, we explore optimization games, in which the value of the characteristic function is provided as the optimal value of an optimization problem. To assess the robustness of the allocation methods, we use the Lipschitz constant, which quantifies the extent of change in the allocation vector in response to a unit perturbation in the weight vector of the underlying problem. Thereafter, we provide an algorithm for the matching game that returns an allocation belonging to the $\left(\frac{1}{2}-ε\right)$-approximate core with Lipschitz constant $O(ε^{-1})$. Additionally, we provide an algorithm for a minimum spanning tree game that returns an allocation belonging to the $4$-approximate core with a constant Lipschitz constant. The Shapley value is a popular allocation that satisfies several desirable properties. Therefore, we investigate the robustness of the Shapley value. We demonstrate that the Lipschitz constant of the Shapley value for the minimum spanning tree is constant, whereas that for the matching game is $Ω(\log n)$, where $n$ denotes the number of vertices.

cs.GT↗

arXiv2024

Testing Spreading Behavior in Networks with Arbitrary Topologies

Inspired by the works of Goldreich and Ron (J. ACM, 2017) and Nakar and Ron (ICALP, 2021), we initiate the study of property testing in dynamic environments with arbitrary topologies. Our focus is on the simplest non-trivial rule that can be tested, which corresponds to the 1-BP rule of bootstrap percolation and models a simple spreading behavior: Every "infected" node stays infected forever, and each "healthy" node becomes infected if and only if it has at least one infected neighbor. We show various results for both the case where we test a single time step of evolution and where the evolution spans several time steps. In the first, we show that the worst-case query complexity is $O(Δ/\varepsilon)$ or $\tilde{O}(\sqrt{n}/\varepsilon)$ (whichever is smaller), where $Δ$ and $n$ are the maximum degree of a node and number of vertices, respectively, in the underlying graph, and we also show lower bounds for both one- and two-sided error testers that match our upper bounds up to $Δ= o(\sqrt{n})$ and $Δ= O(n^{1/3})$, respectively. In the second setting of testing the environment over $T$ time steps, we show upper bounds of $O(Δ^{T-1}/\varepsilon T)$ and $\tilde{O}(|E|/\varepsilon T)$, where $E$ is the set of edges of the underlying graph. All of our algorithms are one-sided error, and all of them are also time-conforming and non-adaptive, with the single exception of the more complex $\tilde{O}(\sqrt{n}/\varepsilon)$-query tester for the case $T = 2$.

cs.DC↗

arXiv2024

PMSM transient response optimization by end-to-end optimal control

Speed responses of motors, especially Permanent Magnet Synchronous Motors (PMSMs), are increasing in importance for recent applications, such as electric vehicles or quadrotors. These applications require quick acceleration performance. However, commercial controllers are based mainly on Proportional-Integral (PI) controllers, which are suitable for eliminating steady-state errors but unsuitable for transient response optimization. In this paper, we replaced whole conventional controllers with an end-to-end Recurrent Neural Network (RNN) that has a regularized transition matrix. Our end-to-end controller directly minimizes the transient response time on the basis of optimal control theory. Computer-simulated results show that speed response indices improved using the RNN rather than a PI controller, while both were under comparable power losses. The current vector trajectories of the RNN showed that the RNN could automatically determine arbitrary trajectories in the flux-weakening region in accordance with an arbitrarily designed loss function. In contrast, the traditional flux-weakening methods using PI controllers have pre-determined current vector trajectories.

eess.SY↗

arXiv2024

Controlling Posterior Collapse by an Inverse Lipschitz Constraint on the Decoder Network

Variational autoencoders (VAEs) are one of the deep generative models that have experienced enormous success over the past decades. However, in practice, they suffer from a problem called posterior collapse, which occurs when the encoder coincides, or collapses, with the prior taking no information from the latent structure of the input data into consideration. In this work, we introduce an inverse Lipschitz neural network into the decoder and, based on this architecture, provide a new method that can control in a simple and clear manner the degree of posterior collapse for a wide range of VAE models equipped with a concrete theoretical guarantee. We also illustrate the effectiveness of our method through several numerical experiments.

cs.LG↗

arXiv2023

Online Algorithms for Spectral Hypergraph Sparsification

We provide the first online algorithm for spectral hypergraph sparsification. In the online setting, hyperedges with positive weights are arriving in a stream, and upon the arrival of each hyperedge, we must irrevocably decide whether or not to include it in the sparsifier. Our algorithm produces an $(ε, δ)$-spectral sparsifier with multiplicative error $ε$ and additive error $δ$ that has $O(ε^{-2} n \log n \log r \log(1 + εW/δn))$ hyperedges with high probability, where $ε, δ\in (0,1)$, $n$ is the number of nodes, and $W$ is the sum of edge weights. The space complexity of our algorithm is $O(n^2)$, while previous algorithms require the space complexity of $Ω(m)$, where $m$ is the number of hyperedges. This provides an exponential improvement in the space complexity since $m$ can be exponential in $n$.

cs.DS↗

arXiv2023

A Batch-to-Online Transformation under Random-Order Model

We introduce a transformation framework that can be utilized to develop online algorithms with low $ε$-approximate regret in the random-order model from offline approximation algorithms. We first give a general reduction theorem that transforms an offline approximation algorithm with low average sensitivity to an online algorithm with low $ε$-approximate regret. We then demonstrate that offline approximation algorithms can be transformed into a low-sensitivity version using a coreset construction method. To showcase the versatility of our approach, we apply it to various problems, including online $(k,z)$-clustering, online matrix approximation, and online regression, and successfully achieve polylogarithmic $ε$-approximate regret for each problem. Moreover, we show that in all three cases, our algorithm also enjoys low inconsistency, which may be desired in some online applications.

cs.LG↗

arXiv2023

Lipschitz Continuous Algorithms for Graph Problems

Graph algorithms are widely used for decision making and knowledge discovery. To ensure their effectiveness, it is essential that their output remains stable even when subjected to small perturbations to the input because frequent output changes can result in costly decisions, reduced user trust, potential security concerns, and lack of replicability. In this study, we consider the Lipschitz continuity of algorithms as a stability measure and initiate a systematic study of the Lipschitz continuity of algorithms for (weighted) graph problems. Depending on how we embed the output solution to a metric space, we can think of several Lipschitzness notions. We mainly consider the one that is invariant under scaling of weights, and we provide Lipschitz continuous algorithms and lower bounds for the minimum spanning tree problem, the shortest path problem, and the maximum weight matching problem. In particular, our shortest path algorithm is obtained by first designing an algorithm for unweighted graphs that are robust against edge contractions and then applying it to the unweighted graph constructed from the original weighted graph. Then, we consider another Lipschitzness notion induced by a natural mapping that maps the output solution to its characteristic vector. It turns out that no Lipschitz continuous algorithm exists for this Lipschitz notion, and we instead design algorithms with bounded pointwise Lipschitz constants for the minimum spanning tree problem and the maximum weight bipartite matching problem. Our algorithm for the latter problem is based on an LP relaxation with entropy regularization.

cs.DS↗

arXiv2023

Ordered Graph Limits and Their Applications

The emerging theory of graph limits exhibits an analytic perspective on graphs, showing that many important concepts and tools in graph theory and its applications can be described more naturally (and sometimes proved more easily) in analytic language. We extend the theory of graph limits to the ordered setting, presenting a limit object for dense vertex-ordered graphs, which we call an orderon. As a special case, this yields limit objects for matrices whose rows and columns are ordered, and for dynamic graphs that expand (via vertex insertions) over time. Along the way, we devise an ordered locality-preserving variant of the cut distance between ordered graphs, showing that two graphs are close with respect to this distance if and only if they are similar in terms of their ordered subgraph frequencies. We show that the space of orderons is compact with respect to this distance notion, which is key to a successful analysis of combinatorial objects through their limits. We derive several applications of the ordered limit theory in extremal combinatorics, sampling, and property testing in ordered graphs. In particular, we prove a new ordered analogue of the well-known result by Alon and Stav [RS\&A'08] on the furthest graph from a hereditary property; this is the first known result of this type in the ordered setting. Unlike the unordered regime, here the random graph model $G(n, p)$ with an ordering over the vertices is not always asymptotically the furthest from the property for some $p$. However, using our ordered limit theory, we show that random graphs generated by a stochastic block model, where the blocks are consecutive in the vertex ordering, are (approximately) the furthest. Additionally, we describe an alternative analytic proof of the ordered graph removal lemma [Alon et al., FOCS'17].

math.CO↗

arXiv2023

The Secretary Problem with Predictions

The value maximization version of the secretary problem is the problem of hiring a candidate with the largest value from a randomly ordered sequence of candidates. In this work, we consider a setting where predictions of candidate values are provided in advance. We propose an algorithm that achieves a nearly optimal value if the predictions are accurate and results in a constant-factor competitive ratio otherwise. We also show that the worst-case competitive ratio of an algorithm cannot be higher than some constant $< 1/\mathrm{e}$, which is the best possible competitive ratio when we ignore predictions, if the algorithm performs nearly optimally when the predictions are accurate. Additionally, for the multiple-choice secretary problem, we propose an algorithm with a similar theoretical guarantee. We empirically illustrate that if the predictions are accurate, the proposed algorithms perform well; meanwhile, if the predictions are inaccurate, performance is comparable to existing algorithms that do not use predictions.

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arXiv2022

Sublinear-Time Algorithms for Max Cut, Max E2Lin$(q)$, and Unique Label Cover on Expanders

We show sublinear-time algorithms for Max Cut and Max E2Lin$(q)$ on expanders in the adjacency list model that distinguishes instances with the optimal value more than $1-\varepsilon$ from those with the optimal value less than $1-ρ$ for $ρ\gg \varepsilon$. The time complexities for Max Cut and Max $2$Lin$(q)$ are $\widetilde{O}(\frac{1}{ϕ^2ρ} \cdot m^{1/2+O(\varepsilon/(ϕ^2ρ))})$ and $\widetilde{O}(\mathrm{poly}(\frac{q}{ϕρ})\cdot {(mq)}^{1/2+O(q^6\varepsilon/ϕ^2ρ^2)})$, respectively, where $m$ is the number of edges in the underlying graph and $ϕ$ is its conductance. Then, we show a sublinear-time algorithm for Unique Label Cover on expanders with $ϕ\gg ε$ in the bounded-degree model. The time complexity of our algorithm is $\widetilde{O}_d(2^{q^{O(1)}\cdotϕ^{1/q}\cdot \varepsilon^{-1/2}}\cdot n^{1/2+q^{O(q)}\cdot \varepsilon^{4^{1.5-q}}\cdot ϕ^{-2}})$, where $n$ is the number of variables. We complement these algorithmic results by showing that testing $3$-colorability requires $Ω(n)$ queries even on expanders.

cs.DS↗

arXiv2022

Low Degree Testing over the Reals

We study the problem of testing whether a function $f: \mathbb{R}^n \to \mathbb{R}$ is a polynomial of degree at most $d$ in the \emph{distribution-free} testing model. Here, the distance between functions is measured with respect to an unknown distribution $\mathcal{D}$ over $\mathbb{R}^n$ from which we can draw samples. In contrast to previous work, we do not assume that $\mathcal{D}$ has finite support. We design a tester that given query access to $f$, and sample access to $\mathcal{D}$, makes $(d/\varepsilon)^{O(1)}$ many queries to $f$, accepts with probability $1$ if $f$ is a polynomial of degree $d$, and rejects with probability at least $2/3$ if every degree-$d$ polynomial $P$ disagrees with $f$ on a set of mass at least $\varepsilon$ with respect to $\mathcal{D}$. Our result also holds under mild assumptions when we receive only a polynomial number of bits of precision for each query to $f$, or when $f$ can only be queried on rational points representable using a logarithmic number of bits. Along the way, we prove a new stability theorem for multivariate polynomials that may be of independent interest.

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