arXiv subjects

Tsubasa Harada

Publications and source records attributed to Tsubasa Harada.

6 recordsLinked to original sources

arXiv2025

Online Algorithms for Repeated Optimal Stopping: Balancing Baseline Guarantees and Regret

We study the repeated optimal stopping problem, in which the same optimal stopping instance with an unknown distribution is solved repeatedly over $T$ rounds. We aim to simultaneously achieve strong per-round performance guarantees relative to a given baseline and sublinear regret across all rounds. Our primary contribution is a comprehensive theoretical characterization of whether and when these two objectives are compatible. First, under standard semi-bandit feedback, we prove that maintaining the per-round guarantee forces regret of $\Omega(T / \log T)$. Second, even under full feedback, we show that requiring almost-sure satisfaction of the per-round guarantee in every round is incompatible with sublinear regret. Third, under full feedback, we propose a general algorithmic framework that achieves both sublinear regret and the per-round guarantee with high probability. Our framework applies to canonical problems, including the prophet inequality, the secretary problem, and their variants under adversarial, random, and i.i.d. input models. For example, in the repeated prophet inequality problem, our method guarantees that, with high probability in each round, its expected reward is at least that of the classical single-sample algorithm, which achieves a $1/2$ competitive ratio, while simultaneously ensuring $\tilde{O}(\sqrt{T})$ regret. Furthermore, we establish a regret lower bound of $\Omega(\sqrt{T})$ even in the i.i.d. model, which is nearly tight with respect to the number of rounds.

cs.DS↗

arXiv2025

Bandit Max-Min Fair Allocation

In this paper, we study a new decision-making problem called the bandit max-min fair allocation (BMMFA) problem. The goal of this problem is to maximize the minimum utility among agents with additive valuations by repeatedly assigning indivisible goods to them. One key feature of this problem is that each agent's valuation for each item can only be observed through the semi-bandit feedback, while existing work supposes that the item values are provided at the beginning of each round. Another key feature is that the algorithm's reward function is not additive with respect to rounds, unlike most bandit-setting problems. Our first contribution is to propose an algorithm that has an asymptotic regret bound of $O(m\sqrt{T}\ln T/n + m\sqrt{T \ln(mnT)})$, where $n$ is the number of agents, $m$ is the number of items, and $T$ is the time horizon. This is based on a novel combination of bandit techniques and a resource allocation algorithm studied in the literature on competitive analysis. Our second contribution is to provide the regret lower bound of $\Omega(m\sqrt{T}/n)$. When $T$ is sufficiently larger than $n$, the gap between the upper and lower bounds is a logarithmic factor of $T$.

cs.LG↗

arXiv2024

A Nearly Optimal Deterministic Algorithm for Online Transportation Problem

For the online transportation problem with $m$ server sites, it has long been known that the competitive ratio of any deterministic algorithm is at least $2m-1$. Kalyanasundaram and Pruhs conjectured in 1998 that a deterministic $(2m-1)$-competitive algorithm exists for this problem, a conjecture that has remained open for over two decades. In this paper, we propose a new deterministic algorithm named Subtree-Decomposition for the online transportation problem and show that it achieves a competitive ratio of at most $8m-5$. This is the first $O(m)$-competitive deterministic algorithm, coming close to the lower bound of $2m-1$ within a constant factor.

cs.DS↗

arXiv2024

A Lower Bound on the Competitive Ratio of the Permutation Algorithm for Online Facility Assignment on a Line

In the online facility assignment on a line (OFAL) with a set $S$ of $k$ servers and a capacity $c:S\to\mathbb{N}$, each server $s\in S$ with a capacity $c(s)$ is placed on a line and a request arrives on a line one-by-one. The task of an online algorithm is to irrevocably assign a current request to one of the servers with vacancies before the next request arrives. An algorithm can assign up to $c(s)$ requests to each server $s\in S$. In this paper, we show that the competitive ratio of the permutation algorithm is at least $k+1$ for OFAL where the servers are evenly placed on a line. This disproves the result that the permutation algorithm is $k$-competitive by Ahmed et al..

cs.DS↗

arXiv2023

Competitive Analysis of Online Facility Assignment for General Layout of Servers on a Line

In the online facility assignment on a line ${\rm OFAL}(S,c)$ with a set $S$ of $k$ servers and a capacity $c:S\to\mathbb{N}$, each server $s\in S$ with a capacity $c(s)$ is placed on a line, and a request arrives on a line one-by-one. The task of an online algorithm is to irrevocably match a current request with one of the servers with vacancies before the next request arrives. An algorithm can match up to $c(s)$ requests to a server $s\in S$. In this paper, we propose a new online algorithm PTCP (Policy Transition at Critical Point) for $\mathrm{OFAL}(S,c)$ and show that PTCP is $(2\alpha(S)+1)$-competitive, where $\alpha(S)$ is informally the ratio of the diameter of $S$ to the maximum distance between two adjacent servers in $S$. Depending on the layout of servers, $\alpha(S)$ ranges from constant (independent of $k$) to $k-1$. Among all of known algorithms for $\mathrm{OFAL}(S,c)$, this upper bound on the competitive ratio is the best when $\alpha(S)$ is small. We also show that the competitive ratio of any MPFS (Most Preferred Free Servers) algorithm is at least $2\alpha(S)+1$. For $\mathrm{OFAL}(S,c)$, recall that MPFS is a class of algorithms whose competitive ratio does not depend on a capacity $c$ and it includes the natural greedy algorithm and PTCP, etc. Thus, this implies that PTCP is the best for $\mathrm{OFAL}(S,c)$ in the class MPFS.

cs.DS↗

arXiv2022

Capacity-Insensitive Algorithms for Online Facility Assignment Problems on a Line

In the online facility assignment problem OFA(k,\ell), there exist k servers with a capacity \ell \geq 1 on a metric space and a request arrives one-by-one. The task of an online algorithm is to irrevocably match a current request with one of the servers with vacancies before the next request arrives. As special cases for OFA(k,\ell), we consider OFA(k,\ell) on a line, which is denoted by OFAL(k,\ell) and OFAL_{eq}(k,\ell), where the latter is the case of OFAL(k,\ell) with equidistant servers. In this paper, we deal with the competitive analysis for the above problems. As a natural generalization of the greedy algorithm GRDY, we introduce a class of algorithms called MPFS (most preferred free servers) and show that any MPFS algorithm has the capacity-insensitive property, i.e., for any \ell \geq 1, ALG is c-competitive for OFA(k,1) iff ALG is c-competitive for OFA(k,\ell). By applying the capacity-insensitive property of the greedy algorithm GRDY, we derive the matching upper and lower bounds 4k-5 on the competitive ratio of GRDY for OFAL_{eq}(k,\ell). To investigate the capability of MPFS algorithms, we show that the competitive ratio of any MPFS algorithm ALG for OFAL_{eq}(k,\ell) is at least $2k-1$. Then we propose a new MPFS algorithm IDAS (Interior Division for Adjacent Servers) for OFAL(k,\ell) and show that the competitive ratio of IDAS for OFAL}_{eq}(k,\ell) is at most 2k-1, i.e., IDAS for OFAL_{eq}(k,\ell) is best possible in all the MPFS algorithms.

cs.DS↗