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

Portfolio optimization tasks describe sequential decision problems in which the investor’s wealth is distributed across a set of assets. Allocation constraints are used to enforce minimal or maximal investments into particular subsets of assets to control for objectives such as limiting the portfolio’s exposure to a certain sector due to environmental concerns. Although methods for (CRL) can optimize policies while considering allocation constraints, it can be observed that these general methods yield suboptimal results. In this paper, we propose a novel approach to handle allocation constraints based on a decomposition of the constraint action space into a set of unconstrained allocation problems. In particular, we examine this approach for the case of two constraints. For example, an investor may wish to invest at least a certain percentage of the portfolio into green technologies while limiting the investment in the fossil energy sector. We show that the action space of the task is equivalent to the decomposed action space, and introduce a new (RL) approach CAOSD, which is built on top of the decomposition. The experimental evaluation on real-world Nasdaq data demonstrates that our approach consistently outperforms state-of-the-art CRL benchmarks for portfolio optimization.

Abstract Financial portfolio managers typically face multi-period optimization tasks such as short-selling or investing at least a particular portion of the portfolio in a specific industry sector. A common approach to tackle these problems is to use constrained Markov decision process (CMDP) methods, which may suffer from sample inefficiency, hyperparameter tuning, and lack of guarantees for constraint violations. In this paper, we propose Action Space Decomposition Based Optimization (ADBO) for optimizing a more straightforward surrogate task that allows actions to be mapped back to the original task. We examine our method on two real-world data portfolio construction tasks. The results show that our new approach consistently outperforms state-of-the-art benchmark approaches for general CMDPs.