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Efficient allocation of resources to activities is pivotal in executing business processes but remains challenging. While resource allocation methodologies are well-established in domains like manufacturing, their application within business process management remains limited. Existing methods often do not scale well to large processes with numerous activities or optimize across multiple cases. This paper aims to address this gap by proposing two learning-based methods for resource allocation in business processes. The first method leverages Deep Reinforcement Learning (DRL) to learn near-optimal policies by taking action in the business process. The second method is a score-based value function approximation approach, which learns the weights of a set of curated features to prioritize resource assignments. To evaluate the proposed approaches, we first designed six distinct business processes with archetypal process flows and characteristics. These business processes were then connected to form three realistically sized business processes. We benchmarked our methods against traditional heuristics and existing resource allocation methods. The results show that our methods learn adaptive resource allocation policies that outperform or are competitive with the benchmarks in five out of six individual business processes. The DRL approach outperforms all benchmarks in all three composite business processes and finds a policy that is, on average, 13.1% better than the best-performing benchmark.