On-Policy and Off-Policy Learning for Large Action Spaces

Automated decision-making algorithms drive applications such as recommendation systems and search engines. These algorithms often rely on off-policy contextual bandits or off-policy learning (OPL). Conventionally, OPL selects actions that maximize the expected reward from an existing action set. However, in many real-world scenarios, actions, such as news articles or video content, change continuously, and the action space evolves over time after data collection. We define actions introduced after deploying the logging policy as new actions and focus on OPL with new actions. Existing OPL methods identify optimal actions from the existing set effectively but cannot learn and select new actions because no relevant data are logged. To address this limitation, we propose a new OPL method that leverages action features. We first introduce the Local Combination PseudoInverse (LCPI) estimator for the policy gradient, generalizing the PseudoInverse estimator initially proposed for off-policy evaluation of slate bandits. LCPI controls the trade-off between reward-modeling condition and the condition for data collection regarding the action features, capturing the interaction effects among different dimensions of action features. Furthermore, we propose a generalized algorithm called Policy Optimization for Effective New Actions (PONA), which integrates LCPI, a component specialized for new action selection, with Doubly Robust (DR), which excels at learning within existing actions. We define PONA as a weighted sum of the LCPI and DR estimators, optimizing both the selection of existing and new actions, and allowing the proportion of new action selections to be adjusted by the weight parameter. Through extensive experiments, we demonstrate that PONA efficiently selects new actions while maintaining the overall policy performance as opposed to most existing methods that cannot select new actions.

We study risk-aware offline policy learning, aiming to learn a decision rule from logged data that is optimal under general risk criteria. This problem is crucial in high-stakes domains where online interaction is infeasible and adverse outcomes must be carefully controlled. However, existing literature on offline contextual bandits either centers on expected-reward criteria or restricts risk considerations to policy evaluation instead of optimization. In this work, we propose a unified distributional framework for optimizing Lipschitz-continuous risk functionals, a broad class of risk measures encompassing mean-variance, entropic risk, and conditional value-at-risk, among others. By developing novel empirical concentration inequalities for importance sampling-based distributional estimators, our analysis derives data-dependent suboptimality bounds with an $\tilde{\mathcal{O}}(1/\sqrt{n})$ rate, without relying on restrictive uniform overlap assumptions. This rate is minimax optimal and matches that of risk-neutral offline policy optimization, indicating that optimizing general Lipschitz risk criteria incurs no additional statistical cost relative to the expected-reward.

We study PAC learning in tabular discounted Markov decision processes with exogenous i.i.d. contexts, with discount factor $γ$, finite state space $\mathcal X$, action space $\mathcal A$, and context space $\mathcal Z$. At each time step, a context is drawn independently from an unknown distribution $μ$ and revealed before the agent acts. This context may affect both rewards and transitions, while remaining uncontrolled by the agent. Depending on the regime, the learner has access either to a sampling oracle for $μ$, to a sampling oracle for the transition kernel conditioned on state-context-action tuples, or to both. Oracles can be accessed before and during policy execution. The sample complexity is measured by a couple $(n,m)$, where $n$ is the number of calls to the sampling oracles before execution and $m$ is the number of calls to the sampling oracles during execution. When rewards and transitions are known and only the context distribution $μ$ is sampled, we give a variance-reduced algorithm that solves policy evaluation (PE), best-value estimation (BVE), and best-policy extraction (BPE) with $\left(\widetilde O\left(1/((1-γ)^3\varepsilon^2)\right), 0 \right)$ sample complexity. The rate is independent of $|\mathcal Z|$ and minimax optimal up to logarithmic factors. As a corollary, we also obtain tight rates in the case of one-step perfect look-ahead, improving upon the existing guarantees. In the fully unknown regime, where both $μ$ and P must be learned, we show that PE remains $|\mathcal Z|$-free, with matching upper and lower bounds $\bigl(\widetilde O(|\mathcal X|/((1-γ)^3\varepsilon^2)),\, \widetilde O(1/((1-γ)^2\varepsilon^2))\bigr)$.