Allocation tasks represent a class of problems where a limited amount of resources must be allocated to a set of entities at each time step. Prominent examples of this task include portfolio optimization or distributing computational workloads across servers.Allocation tasks are typically bound by linear constraints describing practical requirements that have to be strictly fulfilled at all times. In portfolio optimization, for example, investors may be obligated to allocate less than 30\% of the funds into a certain industrial sector in any investment period. Such constraints restrict the action space of allowed allocations in intricate ways, which makes learning a policy that avoids constraint violations difficult.In this paper, we propose a new method for constrained allocation tasks based on an autoregressive process to sequentially sample allocations for each entity. In addition, we introduce a novel de-biasing mechanism to counter the initial bias caused by sequential sampling. We demonstrate the superior performance of our approach compared to a variety of Constrained Reinforcement Learning (CRL) methods on three distinct constrained allocation tasks: portfolio optimization, computational workload distribution, and a synthetic allocation benchmark. Our code is available at: https://github.com/niklasdbs/paspo

Continuous allocation tasks are a class of problems where an agent needs to distribute a limited amount of resources over a set of entities at each time step.

Continuous allocation tasks are a class of problems where an agent needs to distribute a limited amount of resources over a set of entities at each time step.

Allocation tasks represent a class of problems where a limited amount of resources must be allocated to a set of entities at each time step. Prominent examples of this task include portfolio optimization or distributing computational workloads across servers. Allocation tasks are typically bound by linear constraints describing practical requirements that have to be strictly fulfilled at all times. In portfolio optimization, for example, investors may be obligated to allocate less than 30\% of the funds into a certain industrial sector in any investment period. Such constraints restrict the action space of allowed allocations in intricate ways, which makes learning a policy that avoids constraint violations difficult. In this paper, we propose a new method for constrained allocation tasks based on an autoregressive process to sequentially sample allocations for each entity. In addition, we introduce a novel de-biasing mechanism to counter the initial bias caused by sequential sampling. We demonstrate the superior performance of our approach compared to a variety of Constrained Reinforcement Learning (CRL) methods on three distinct constrained allocation tasks: portfolio optimization, computational workload distribution, and a synthetic allocation benchmark. Our code is available at: https://github.com/niklasdbs/paspo

Prediction models have been widely adopted as the basis for decision-making in domains as diverse as employment, education, lending, and health. Yet, few real world problems readily present themselves as precisely formulated prediction tasks. In particular, there are often many reasonable target variable options. Prior work has argued that this is an important and sometimes underappreciated choice, and has also shown that target choice can have a significant impact on the fairness of the resulting model. However, the existing literature does not offer a formal framework for characterizing the extent to which target choice matters in a particular task. Our work fills this gap by drawing connections between the problem of target choice and recent work on predictive multiplicity. Specifically, we introduce a conceptual and computational framework for assessing how the choice of target affects individuals' outcomes and selection rate disparities across groups. We call this multi-target multiplicity. Along the way, we refine the study of single-target multiplicity by introducing notions of multiplicity that respect resource constraints -- a feature of many real-world tasks that is not captured by existing notions of predictive multiplicity. We apply our methods on a healthcare dataset, and show that the level of multiplicity that stems from target variable choice can be greater than that stemming from nearly-optimal models of a single target.

Prescribing optimal operation based on the condition of the system and, thereby, potentially prolonging the remaining useful lifetime has a large potential for actively managing the availability, maintenance and costs of complex systems. Reinforcement learning (RL) algorithms are particularly suitable for this type of problems given their learning capabilities. A special case of a prescriptive operation is the power allocation task, which can be considered as a sequential allocation problem, where the action space is bounded by a simplex constraint. A general continuous action-space solution of such sequential allocation problems has still remained an open research question for RL algorithms. In continuous action-space, the standard Gaussian policy applied in reinforcement learning does not support simplex constraints, while the Gaussian-softmax policy introduces a bias during training. In this work, we propose the Dirichlet policy for continuous allocation tasks and analyze the bias and variance of its policy gradients. We demonstrate that the Dirichlet policy is bias-free and provides significantly faster convergence, better performance and better hyperparameters robustness over the Gaussian-softmax policy. Moreover, we demonstrate the applicability of the proposed algorithm on a prescriptive operation case, where we propose the Dirichlet power allocation policy and evaluate the performance on a case study of a set of multiple lithium-ion (Li-I) battery systems. The experimental results show the potential to prescribe optimal operation, improve the efficiency and sustainability of multi-power source systems.