Efficient Feel-Good Thompson Sampling for Contextual Dueling Bandits

Kernekoncepter

The core message of this paper is to propose a new algorithm, FGTS.CDB, for linear contextual dueling bandits based on the Feel-Good Thompson sampling technique. The algorithm achieves a nearly minimax-optimal regret bound of e
O(d√T), where d is the feature dimensionality and T is the number of rounds.

Resumé

The paper proposes a new algorithm, FGTS.CDB, for the problem of linear contextual dueling bandits. The key aspects are:

The algorithm is based on the Feel-Good Thompson sampling technique, which is a variant of the standard Thompson sampling approach. The core idea is to introduce a new "Feel-Good" exploration term in the likelihood function that encourages exploration of arms with high rewards in previous rounds.

The Feel-Good exploration term in FGTS.CDB is specifically designed for the dueling bandit setting, containing an additional inner product term between the current model parameter and the feature vector of the adversarial arm. This term plays a crucial role in the analysis by eliminating cross terms that arise from the comparison of actions.

The authors prove that FGTS.CDB achieves a nearly minimax-optimal regret bound of e
O(d√T), matching the lower bound for linear contextual dueling bandits. This is the first algorithm based on Thompson sampling that can achieve such an optimal regret guarantee in this setting.

The authors also extend the analysis to the case of general nonlinear reward functions and recover the regret bound for several cases of interest, including finite action sets and finite model sets.

Experiments on synthetic data show that FGTS.CDB significantly outperforms existing UCB-based algorithms for contextual dueling bandits, including MaxInP, CoLSTIM, and VACDB.

Statistik

The paper does not contain any explicit numerical data or statistics. The key results are the regret bounds derived for the proposed FGTS.CDB algorithm.

Citater

None.

Vigtigste indsigter udtrukket fra

Feel-Good Thompson Sampling for Contextual Dueling Bandits

by Xuheng Li,He... kl. arxiv.org 04-10-2024

https://arxiv.org/pdf/2404.06013.pdf

Dybere Forespørgsler

How can the ideas of FGTS.CDB be extended to other variants of dueling bandits, such as those with Copeland winners or Borda winners

To extend the ideas of FGTS.CDB to other variants of dueling bandits, such as those with Copeland winners or Borda winners, we can modify the arm selection scheme and the likelihood function to accommodate the specific characteristics of these variants.
For Copeland winners, where the goal is to identify the action that wins the most pairwise comparisons, we can adjust the arm selection criteria to maximize the number of victories over other actions. The likelihood function can be tailored to capture the pairwise comparison outcomes in a way that reflects the Copeland winner model.
Similarly, for Borda winners, where the goal is to identify the action with the highest cumulative score based on rankings, the arm selection scheme can prioritize actions that are likely to receive higher rankings. The likelihood function can be designed to consider the ranking information and the cumulative scores of the actions.
By customizing the arm selection and likelihood functions to align with the specific requirements of Copeland winners or Borda winners, FGTS.CDB can be adapted to effectively address these variants of dueling bandits.

Can a variance-aware version of FGTS.CDB be developed to further improve the empirical performance

Developing a variance-aware version of FGTS.CDB could potentially enhance its empirical performance by incorporating variance information into the exploration-exploitation trade-off. By considering the variance of the reward estimates along with the mean estimates, the algorithm can make more informed decisions about which arms to select for exploration.
One approach to creating a variance-aware version of FGTS.CDB could involve modifying the likelihood function to incorporate variance terms or introducing additional exploration terms that account for the uncertainty in the reward estimates. By balancing the exploration of high-variance arms with the exploitation of low-variance arms, the algorithm could potentially achieve better regret bounds and improved performance in practice.
By integrating variance-aware techniques into FGTS.CDB, the algorithm could adapt more dynamically to the uncertainty in the reward estimates and make more efficient decisions in the contextual dueling bandit setting.

What are the potential applications of the contextual dueling bandit framework beyond preference-based reinforcement learning, and how can FGTS.CDB be adapted to those settings

The contextual dueling bandit framework has applications beyond preference-based reinforcement learning in various domains such as online advertising, personalized recommendation systems, and clinical trials.
In online advertising, contextual dueling bandits can be used to optimize ad selection based on user preferences and contextual information. FGTS.CDB can be adapted to this setting by incorporating features related to ad content, user demographics, and historical interactions to make informed decisions about which ads to display.
In personalized recommendation systems, contextual dueling bandits can help recommend products or content tailored to individual preferences. FGTS.CDB can be leveraged to explore different recommendation options and learn user preferences efficiently over time.
In clinical trials, contextual dueling bandits can be applied to optimize treatment selection for patients based on contextual factors and feedback on treatment outcomes. FGTS.CDB can be adapted to this setting to guide the selection of treatments that are most likely to be effective for individual patients.
By adapting FGTS.CDB to these diverse applications of contextual dueling bandits, it can facilitate more effective decision-making and optimization in real-world scenarios beyond preference-based reinforcement learning.