We first show that a unique optimal policy may not exist if preferences over trajectories are deterministic for PbRL.

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SOI by directly leveraging human feedback without being restricted by a predefined reward model nor cumbersome model selection.

We first show that a unique optimal policy may not exist if preferences over trajectories are deterministic for PbRL.

Recent work on deriving O(log T) anytime regret bounds for stochastic dueling bandit problems has considered mostly Condorcet winners, which do not always exist, and more recently, winners defined by the Copeland set, which do always exist. In this work, we consider a broad notion of winners defined by tournament solutions in social choice theory, which include the Copeland set as a special case but also include several other notions of winners such as the top cycle, uncovered set, and Banks set, and which, like the Copeland set, always exist. We develop a family of UCB-style dueling bandit algorithms for such general tournament solutions, and show O(log T) anytime regret bounds for them. Experiments confirm the ability of our algorithms to achieve low regret relative to the target winning set of interest.

Optimization problems find widespread use in both single-objective and multiobjective scenarios. In practical applications, users aspire for solutions that converge to the region of interest (ROI) along the Pareto front (PF). While the conventional approach involves approximating a fitness function or an objective function to reflect user preferences, this paper explores an alternative avenue. Specifically, we aim to discover a method that sidesteps the need for calculating the fitness function, relying solely on human feedback. Our proposed approach entails conducting direct preference learning facilitated by an active dueling bandit algorithm. The experimental phase is structured into three sessions. Firstly, we assess the performance of our active dueling bandit algorithm. Secondly, we implement our proposed method within the context of Multi-objective Evolutionary Algorithms (MOEAs). This research presents a novel interactive preference-based MOEA framework that not only addresses the limitations of traditional techniques but also unveils new possibilities for optimization problems. In optimization problems, algorithms typically converge to the Pareto front (PF), yet users aim for convergence in their specific region of interest (ROI).

Preference-based Reinforcement Learning (PbRL) replaces reward values in traditional reinforcement learning by preferences to better elicit human opinion on the target objective, especially when numerical reward values are hard to design or interpret. Despite promising results in applications, the theoretical understanding of PbRL is still in its infancy. In this paper, we present the first finite-time analysis for general PbRL problems. We first show that a unique optimal policy may not exist if preferences over trajectories are deterministic for PbRL. If preferences are stochastic, and the preference probability relates to the hidden reward values, we present algorithms for PbRL, both with and without a simulator, that are able to identify the best policy up to accuracy $\varepsilon$ with high probability. Our method explores the state space by navigating to under-explored states, and solves PbRL using a combination of dueling bandits and policy search. Experiments show the efficacy of our method when it is applied to real-world problems.

Recent work on deriving $O(\log T)$ anytime regret bounds for stochastic dueling bandit problems has considered mostly Condorcet winners, which do not always exist, and more recently, winners defined by the Copeland set, which do always exist. In this work, we consider a broad notion of winners defined by tournament solutions in social choice theory, which include the Copeland set as a special case but also include several other notions of winners such as the top cycle, uncovered set, and Banks set, and which, like the Copeland set, always exist. We develop a family of UCB-style dueling bandit algorithms for such general tournament solutions, and show $O(\log T)$ anytime regret bounds for them. Experiments confirm the ability of our algorithms to achieve low regret relative to the target winning set of interest.