# Multi-Armed Bandits with Generalized Temporally-Partitioned Rewards

## TL;DR

This paper introduces a new multi-armed bandit problem where feedback is delayed and partitioned over time, proposing a novel property, theoretical bounds, an algorithm, and experimental validation.

## Contribution

It formalizes the generalized temporally-partitioned rewards problem, introduces the $eta$-spread property, and provides both lower bounds and an efficient algorithm with improved performance bounds.

## Key findings

- Derived a lower bound on algorithm performance.
- Proposed TP-UCB-FR-G algorithm with upper performance bounds.
- Experimental results validate theoretical claims and algorithm effectiveness.

## Abstract

Decision-making problems of sequential nature, where decisions made in the past may have an impact on the future, are used to model many practically important applications. In some real-world applications, feedback about a decision is delayed and may arrive via partial rewards that are observed with different delays. Motivated by such scenarios, we propose a novel problem formulation called multi-armed bandits with generalized temporally-partitioned rewards. To formalize how feedback about a decision is partitioned across several time steps, we introduce $\beta$-spread property. We derive a lower bound on the performance of any uniformly efficient algorithm for the considered problem. Moreover, we provide an algorithm called TP-UCB-FR-G and prove an upper bound on its performance measure. In some scenarios, our upper bound improves upon the state of the art. We provide experimental results validating the proposed algorithm and our theoretical results.