Doubly robust Thompson sampling for linear payoffs
- URL: http://arxiv.org/abs/2102.01229v3
- Date: Sun, 30 Apr 2023 21:19:54 GMT
- Title: Doubly robust Thompson sampling for linear payoffs
- Authors: Wonyoung Kim, Gi-soo Kim, Myunghee Cho Paik
- Abstract summary: We propose a novel multi-armed contextual bandit algorithm called Doubly Robust (DR) Thompson Sampling.
The proposed algorithm is designed to allow a novel additive regret decomposition leading to an improved regret bound with the order of $tildeO(phi-2sqrtT)$.
- Score: 12.375561840897742
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: A challenging aspect of the bandit problem is that a stochastic reward is
observed only for the chosen arm and the rewards of other arms remain missing.
The dependence of the arm choice on the past context and reward pairs compounds
the complexity of regret analysis. We propose a novel multi-armed contextual
bandit algorithm called Doubly Robust (DR) Thompson Sampling employing the
doubly-robust estimator used in missing data literature to Thompson Sampling
with contexts (\texttt{LinTS}). Different from previous works relying on
missing data techniques (\citet{dimakopoulou2019balanced},
\citet{kim2019doubly}), the proposed algorithm is designed to allow a novel
additive regret decomposition leading to an improved regret bound with the
order of $\tilde{O}(\phi^{-2}\sqrt{T})$, where $\phi^2$ is the minimum
eigenvalue of the covariance matrix of contexts. This is the first regret bound
of \texttt{LinTS} using $\phi^2$ without the dimension of the context, $d$.
Applying the relationship between $\phi^2$ and $d$, the regret bound of the
proposed algorithm is $\tilde{O}(d\sqrt{T})$ in many practical scenarios,
improving the bound of \texttt{LinTS} by a factor of $\sqrt{d}$. A benefit of
the proposed method is that it utilizes all the context data, chosen or not
chosen, thus allowing to circumvent the technical definition of unsaturated
arms used in theoretical analysis of \texttt{LinTS}. Empirical studies show the
advantage of the proposed algorithm over \texttt{LinTS}.
Related papers
- Feel-Good Thompson Sampling for Contextual Dueling Bandits [49.450050682705026]
We propose a Thompson sampling algorithm, named FGTS.CDB, for linear contextual dueling bandits.
At the core of our algorithm is a new Feel-Good exploration term specifically tailored for dueling bandits.
Our algorithm achieves nearly minimax-optimal regret, i.e., $tildemathcalO(dsqrt T)$, where $d$ is the model dimension and $T$ is the time horizon.
arXiv Detail & Related papers (2024-04-09T04:45:18Z) - LC-Tsallis-INF: Generalized Best-of-Both-Worlds Linear Contextual Bandits [38.41164102066483]
This study considers the linear contextual bandit problem with independent and identically distributed contexts.
Our proposed algorithm is based on the Follow-The-Regularized-Leader with the Tsallis entropy and referred to as the $alpha$-textual-Con (LC)-Tsallis-INF.
arXiv Detail & Related papers (2024-03-05T18:59:47Z) - Efficient Frameworks for Generalized Low-Rank Matrix Bandit Problems [61.85150061213987]
We study the generalized low-rank matrix bandit problem, proposed in citelu2021low under the Generalized Linear Model (GLM) framework.
To overcome the computational infeasibility and theoretical restrain of existing algorithms, we first propose the G-ESTT framework.
We show that G-ESTT can achieve the $tildeO(sqrt(d_1+d_2)3/2Mr3/2T)$ bound of regret while G-ESTS can achineve the $tildeO
arXiv Detail & Related papers (2024-01-14T14:14:19Z) - Variance-Aware Regret Bounds for Stochastic Contextual Dueling Bandits [53.281230333364505]
This paper studies the problem of contextual dueling bandits, where the binary comparison of dueling arms is generated from a generalized linear model (GLM)
We propose a new SupLinUCB-type algorithm that enjoys computational efficiency and a variance-aware regret bound $tilde Obig(dsqrtsum_t=1Tsigma_t2 + dbig)$.
Our regret bound naturally aligns with the intuitive expectation in scenarios where the comparison is deterministic, the algorithm only suffers from an $tilde O(d)$ regret.
arXiv Detail & Related papers (2023-10-02T08:15:52Z) - Double Doubly Robust Thompson Sampling for Generalized Linear Contextual
Bandits [8.508198765617198]
We propose a novel contextual bandit algorithm for generalized linear rewards with an $tildeO(sqrtkappa-1 phi T)$ regret over $T$ rounds.
We also provide an $O(kappa-1 phi log (NT) log T)$ regret bound for $N$ arms under a probabilistic margin condition.
arXiv Detail & Related papers (2022-09-15T00:20:38Z) - Squeeze All: Novel Estimator and Self-Normalized Bound for Linear
Contextual Bandits [18.971564419292893]
We propose a linear contextual bandit algorithm with $O(sqrtdTlog T)$ regret bound, where $d$ is the dimension of contexts and $T$ is the time horizon.
Our proposed algorithm is equipped with a novel estimator in which exploration is embedded through explicit randomization.
arXiv Detail & Related papers (2022-06-11T02:43:17Z) - Breaking the $\sqrt{T}$ Barrier: Instance-Independent Logarithmic Regret
in Stochastic Contextual Linear Bandits [10.127456032874978]
We prove an instance (poly) logarithmic regret for contextual bandits with linear payoff.
contexts indeed help to reduce the regret from $sqrtT$ to $polylog(T)$.
arXiv Detail & Related papers (2022-05-19T23:41:46Z) - Stochastic Contextual Dueling Bandits under Linear Stochastic
Transitivity Models [25.336599480692122]
We consider the regret minimization task in a dueling bandits problem with context information.
We propose a computationally efficient algorithm, $texttCoLSTIM$, which makes its choice based on imitating the feedback process.
Our experiments demonstrate its superiority over state-of-art algorithms for special cases of CoLST models.
arXiv Detail & Related papers (2022-02-09T17:44:19Z) - Thresholded Lasso Bandit [70.17389393497125]
Thresholded Lasso bandit is an algorithm that estimates the vector defining the reward function as well as its sparse support.
We establish non-asymptotic regret upper bounds scaling as $mathcalO( log d + sqrtT )$ in general, and as $mathcalO( log d + sqrtT )$ under the so-called margin condition.
arXiv Detail & Related papers (2020-10-22T19:14:37Z) - Stochastic Bandits with Linear Constraints [69.757694218456]
We study a constrained contextual linear bandit setting, where the goal of the agent is to produce a sequence of policies.
We propose an upper-confidence bound algorithm for this problem, called optimistic pessimistic linear bandit (OPLB)
arXiv Detail & Related papers (2020-06-17T22:32:19Z) - Taking a hint: How to leverage loss predictors in contextual bandits? [63.546913998407405]
We study learning in contextual bandits with the help of loss predictors.
We show that the optimal regret is $mathcalO(minsqrtT, sqrtmathcalETfrac13)$ when $mathcalE$ is known.
arXiv Detail & Related papers (2020-03-04T07:36:38Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.