arXiv subjects

Junya Honda

Publications and source records attributed to Junya Honda.

54 records · Page 3Linked to original sources

arXiv2018

Dueling Bandits with Qualitative Feedback

We formulate and study a novel multi-armed bandit problem called the qualitative dueling bandit (QDB) problem, where an agent observes not numeric but qualitative feedback by pulling each arm. We employ the same regret as the dueling bandit (DB) problem where the duel is carried out by comparing the qualitative feedback. Although we can naively use classic DB algorithms for solving the QDB problem, this reduction significantly worsens the performance---actually, in the QDB problem, the probability that one arm wins the duel over another arm can be directly estimated without carrying out actual duels. In this paper, we propose such direct algorithms for the QDB problem. Our theoretical analysis shows that the proposed algorithms significantly outperform DB algorithms by incorporating the qualitative feedback, and experimental results also demonstrate vast improvement over the existing DB algorithms.

stat.ML↗

arXiv2018

Good Arm Identification via Bandit Feedback

We consider a novel stochastic multi-armed bandit problem called {\em good arm identification} (GAI), where a good arm is defined as an arm with expected reward greater than or equal to a given threshold. GAI is a pure-exploration problem that a single agent repeats a process of outputting an arm as soon as it is identified as a good one before confirming the other arms are actually not good. The objective of GAI is to minimize the number of samples for each process. We find that GAI faces a new kind of dilemma, the {\em exploration-exploitation dilemma of confidence}, which is different difficulty from the best arm identification. As a result, an efficient design of algorithms for GAI is quite different from that for the best arm identification. We derive a lower bound on the sample complexity of GAI that is tight up to the logarithmic factor $\mathrm{O}(\log \frac{1}δ)$ for acceptance error rate $δ$. We also develop an algorithm whose sample complexity almost matches the lower bound. We also confirm experimentally that our proposed algorithm outperforms naive algorithms in synthetic settings based on a conventional bandit problem and clinical trial researches for rheumatoid arthritis.

stat.ML↗

arXiv2018

Exploring a potential energy surface by machine learning for characterizing atomic transport

We propose a machine-learning method for evaluating the potential barrier governing atomic transport based on the preferential selection of dominant points for the atomic transport. The proposed method generates numerous random samples of the entire potential energy surface (PES) from a probabilistic Gaussian process model of the PES, which enables defining the likelihood of the dominant points. The robustness and efficiency of the method are demonstrated on a dozen model cases for proton diffusion in oxides, in comparison with a conventional nudge elastic band method.

physics.chem-ph↗

arXiv2017

Fully adaptive algorithm for pure exploration in linear bandits

We propose the first fully-adaptive algorithm for pure exploration in linear bandits---the task to find the arm with the largest expected reward, which depends on an unknown parameter linearly. While existing methods partially or entirely fix sequences of arm selections before observing rewards, our method adaptively changes the arm selection strategy based on past observations at each round. We show our sample complexity matches the achievable lower bound up to a constant factor in an extreme case. Furthermore, we evaluate the performance of the methods by simulations based on both synthetic setting and real-world data, in which our method shows vast improvement over existing methods.

stat.ML↗

arXiv2017

Worst-case Redundancy of Optimal Binary AIFV Codes and their Extended Codes

Binary AIFV codes are lossless codes that generalize the class of instantaneous FV codes. The code uses two code trees and assigns source symbols to incomplete internal nodes as well as to leaves. AIFV codes are empirically shown to attain better compression ratio than Huffman codes. Nevertheless, an upper bound on the redundancy of optimal binary AIFV codes is only known to be 1, which is the same as the bound of Huffman codes. In this paper, the upper bound is improved to 1/2, which is shown to coincide with the worst-case redundancy of the codes. Along with this, the worst-case redundancy is derived in terms of $p_{\max}\geq$1/2, where $p_{\max}$ is the probability of the most likely source symbol. Additionally, we propose an extension of binary AIFV codes, which use $m$ code trees and allow at most $m$-bit decoding delay. We show that the worst-case redundancy of the extended binary AIFV codes is $1/m$ for $m \leq 4.$

cs.IT↗

arXiv2017

Comprehensive Analysis on Exact Asymptotics of Random Coding Error Probability

This paper considers error probabilities of random codes for memoryless channels in the fixed-rate regime. Random coding is a fundamental scheme to achieve the channel capacity and many studies have been conducted for the asymptotics of the decoding error probability. Gallager derived the exact asymptotics (that is, a bound with asymptotically vanishing relative error) of the error probability below the critical rate. On the other hand, exact asymptotics for fixed rate above the critical rate has been unknown except for symmetric channels (in the strong sense) and strongly nonlattice channels. This paper derives the exact asymptotics for general memoryless channels covering all previously unsolved cases. The analysis reveals that strongly symmetric channels and strongly nonlattice channels correspond to two extreme cases and the expression of the asymptotics is much complicated for general channels.

cs.IT↗

arXiv2017

Variable-to-Fixed Length Homophonic Coding Suitable for Asymmetric Channel Coding

In communication through asymmetric channels the capacity-achieving input distribution is not uniform in general. Homophonic coding is a framework to invertibly convert a (usually uniform) message into a sequence with some target distribution, and is a promising candidate to generate codewords with the nonuniform target distribution for asymmetric channels. In particular, a Variable-to-Fixed length (VF) homophonic code can be used as a suitable component for channel codes to avoid decoding error propagation. However, the existing VF homophonic code requires the knowledge of the maximum relative gap of probabilities between two adjacent sequences beforehand, which is an unrealistic assumption for long block codes. In this paper we propose a new VF homophonic code without such a requirement by allowing one-symbol decoding delay. We evaluate this code theoretically and experimentally to verify its asymptotic optimality.

cs.IT↗

arXiv2016

Variable-to-Fixed Length Homophonic Coding with a Modified Shannon-Fano-Elias Code

Homophonic coding is a framework to reversibly convert a message into a sequence with some target distribution. This is a promising tool to generate a codeword with a biased code-symbol distribution, which is required for capacity-achieving communication by asymmetric channels. It is known that asymptotically optimal homophonic coding can be realized by a Fixed-to-Variable (FV) length code using an interval algorithm similar to a random number generator. However, FV codes are not preferable as a component of channel codes since a decoding error propagates to all subsequent codewords. As a solution for this problem an asymptotically optimal Variable-to-Fixed (VF) length homophonic code, dual Shannon-Fano-Elias-Gray (dual SFEG) code, is proposed in this paper. This code can be interpreted as a dual of a modified Shannon-Fano-Elias (SFE) code based on Gray code. It is also shown as a by-product that the modified SFE code, named SFEG code, achieves a better coding rate than the original SFE code in lossless source coding.

cs.IT↗

arXiv2016

Copeland Dueling Bandit Problem: Regret Lower Bound, Optimal Algorithm, and Computationally Efficient Algorithm

We study the K-armed dueling bandit problem, a variation of the standard stochastic bandit problem where the feedback is limited to relative comparisons of a pair of arms. The hardness of recommending Copeland winners, the arms that beat the greatest number of other arms, is characterized by deriving an asymptotic regret bound. We propose Copeland Winners Relative Minimum Empirical Divergence (CW-RMED) and derive an asymptotically optimal regret bound for it. However, it is not known whether the algorithm can be efficiently computed or not. To address this issue, we devise an efficient version (ECW-RMED) and derive its asymptotic regret bound. Experimental comparisons of dueling bandit algorithms show that ECW-RMED significantly outperforms existing ones.

stat.ML↗

arXiv2015

Regret Lower Bound and Optimal Algorithm in Finite Stochastic Partial Monitoring

Partial monitoring is a general model for sequential learning with limited feedback formalized as a game between two players. In this game, the learner chooses an action and at the same time the opponent chooses an outcome, then the learner suffers a loss and receives a feedback signal. The goal of the learner is to minimize the total loss. In this paper, we study partial monitoring with finite actions and stochastic outcomes. We derive a logarithmic distribution-dependent regret lower bound that defines the hardness of the problem. Inspired by the DMED algorithm (Honda and Takemura, 2010) for the multi-armed bandit problem, we propose PM-DMED, an algorithm that minimizes the distribution-dependent regret. PM-DMED significantly outperforms state-of-the-art algorithms in numerical experiments. To show the optimality of PM-DMED with respect to the regret bound, we slightly modify the algorithm by introducing a hinge function (PM-DMED-Hinge). Then, we derive an asymptotically optimal regret upper bound of PM-DMED-Hinge that matches the lower bound.

stat.ML↗

arXiv2015

Almost Instantaneous Fix-to-Variable Length Codes

We propose almost instantaneous fixed-to-variable-length (AIFV) codes such that two (resp. $K-1$) code trees are used if code symbols are binary (resp. $K$-ary for $K \geq 3$), and source symbols are assigned to incomplete internal nodes in addition to leaves. Although the AIFV codes are not instantaneous codes, they are devised such that the decoding delay is at most two bits (resp. one code symbol) in the case of binary (resp. $K$-ary) code alphabet. The AIFV code can attain better average compression rate than the Huffman code at the expenses of a little decoding delay and a little large memory size to store multiple code trees. We also show for the binary and ternary AIFV codes that the optimal AIFV code can be obtained by solving 0-1 integer programming problems.

cs.IT↗

arXiv2015

Regret Lower Bound and Optimal Algorithm in Dueling Bandit Problem

We study the $K$-armed dueling bandit problem, a variation of the standard stochastic bandit problem where the feedback is limited to relative comparisons of a pair of arms. We introduce a tight asymptotic regret lower bound that is based on the information divergence. An algorithm that is inspired by the Deterministic Minimum Empirical Divergence algorithm (Honda and Takemura, 2010) is proposed, and its regret is analyzed. The proposed algorithm is found to be the first one with a regret upper bound that matches the lower bound. Experimental comparisons of dueling bandit algorithms show that the proposed algorithm significantly outperforms existing ones.

stat.ML↗

arXiv2015

Exact Asymptotics for the Random Coding Error Probability

Error probabilities of random codes for memoryless channels are considered in this paper. In the area of communication systems, admissible error probability is very small and it is sometimes more important to discuss the relative gap between the achievable error probability and its bound than to discuss the absolute gap. Scarlett et al. derived a good upper bound of a random coding union bound based on the technique of saddlepoint approximation but it is not proved that the relative gap of their bound converges to zero. This paper derives a new bound on the achievable error probability in this viewpoint for a class of memoryless channels. The derived bound is strictly smaller than that by Scarlett et al. and its relative gap with the random coding error probability (not a union bound) vanishes as the block length increases for a fixed coding rate.

cs.IT↗

arXiv2015

Normal Bandits of Unknown Means and Variances: Asymptotic Optimality, Finite Horizon Regret Bounds, and a Solution to an Open Problem

Consider the problem of sampling sequentially from a finite number of $N \geq 2$ populations, specified by random variables $X^i_k$, $ i = 1,\ldots , N,$ and $k = 1, 2, \ldots$; where $X^i_k$ denotes the outcome from population $i$ the $k^{th}$ time it is sampled. It is assumed that for each fixed $i$, $\{ X^i_k \}_{k \geq 1}$ is a sequence of i.i.d. normal random variables, with unknown mean $μ_i$ and unknown variance $σ_i^2$. The objective is to have a policy $π$ for deciding from which of the $N$ populations to sample form at any time $n=1,2,\ldots$ so as to maximize the expected sum of outcomes of $n$ samples or equivalently to minimize the regret due to lack on information of the parameters $μ_i$ and $σ_i^2$. In this paper, we present a simple inflated sample mean (ISM) index policy that is asymptotically optimal in the sense of Theorem 4 below. This resolves a standing open problem from Burnetas and Katehakis (1996). Additionally, finite horizon regret bounds are given.

stat.ML↗

arXiv2013

Optimality of Thompson Sampling for Gaussian Bandits Depends on Priors

In stochastic bandit problems, a Bayesian policy called Thompson sampling (TS) has recently attracted much attention for its excellent empirical performance. However, the theoretical analysis of this policy is difficult and its asymptotic optimality is only proved for one-parameter models. In this paper we discuss the optimality of TS for the model of normal distributions with unknown means and variances as one of the most fundamental example of multiparameter models. First we prove that the expected regret of TS with the uniform prior achieves the theoretical bound, which is the first result to show that the asymptotic bound is achievable for the normal distribution model. Next we prove that TS with Jeffreys prior and reference prior cannot achieve the theoretical bound. Therefore the choice of priors is important for TS and non-informative priors are sometimes risky in cases of multiparameter models.

math.ST↗

arXiv2012

Finite-time Regret Bound of a Bandit Algorithm for the Semi-bounded Support Model

In this paper we consider stochastic multiarmed bandit problems. Recently a policy, DMED, is proposed and proved to achieve the asymptotic bound for the model that each reward distribution is supported in a known bounded interval, e.g. [0,1]. However, the derived regret bound is described in an asymptotic form and the performance in finite time has been unknown. We inspect this policy and derive a finite-time regret bound by refining large deviation probabilities to a simple finite form. Further, this observation reveals that the assumption on the lower-boundedness of the support is not essential and can be replaced with a weaker one, the existence of the moment generating function.

math.ST↗

arXiv2011

Stochastic Bandit Based on Empirical Moments

In the multiarmed bandit problem a gambler chooses an arm of a slot machine to pull considering a tradeoff between exploration and exploitation. We study the stochastic bandit problem where each arm has a reward distribution supported in a known bounded interval, e.g. [0,1]. For this model, policies which take into account the empirical variances (i.e. second moments) of the arms are known to perform effectively. In this paper, we generalize this idea and we propose a policy which exploits the first d empirical moments for arbitrary d fixed in advance. The asymptotic upper bound of the regret of the policy approaches the theoretical bound by Burnetas and Katehakis as d increases. By choosing appropriate d, the proposed policy realizes a tradeoff between the computational complexity and the expected regret.

math.ST↗

arXiv2010

An Asymptotically Optimal Policy for Finite Support Models in the Multiarmed Bandit Problem

We propose minimum empirical divergence (MED) policy for the multiarmed bandit problem. We prove asymptotic optimality of the proposed policy for the case of finite support models. In our setting, Burnetas and Katehakis has already proposed an asymptotically optimal policy. For choosing an arm our policy uses a criterion which is dual to the quantity used in Burnetas and Katehakis. Our criterion is easily computed by a convex optimization technique and has an advantage in practical implementation. We confirm by simulations that MED policy demonstrates good performance in finite time in comparison to other currently popular policies.

math.ST↗