TLDR: This research introduces a universal method for representing dynamic task assignment problems, especially those with infinite state and action spaces, for Deep Reinforcement Learning (DRL). It proposes ‘assignment graphs’ as a flexible, graph-based feature representation, a method to map existing Petri Net process models to these graphs, and an adaptation of the PPO algorithm to learn policies on these dynamic graph observations. Experimental results show that this approach enables DRL to effectively solve complex assignment problems that are intractable for traditional vector-based methods.
In the world of business processes, efficiently assigning resources to tasks as new tasks and resources become available is a critical challenge. This area, known as dynamic task assignment, is vital for optimizing operations across various industries. Recently, Deep Reinforcement Learning (DRL) has emerged as a leading method for tackling these complex assignment problems.
However, a significant hurdle in applying DRL to these scenarios has been how to effectively represent the ‘state’ of the process and the ‘possible assignments’ so that a neural network can understand them. This becomes particularly difficult when tasks or resources have features with an unlimited number of possible values, leading to what are called ‘infinite state and action spaces’. Traditional DRL approaches often rely on fixed-size input vectors, which struggle to cope with such variability and unboundedness. For instance, if a project’s budget can be any real number, or if the number of available tasks is not fixed, representing this information in a static vector becomes impossible or highly inefficient.
A Novel Approach to Representation
A new research paper, titled “A Universal Approach to Feature Representation in Dynamic Task Assignment Problems”, addresses this fundamental challenge. The authors, Riccardo Lo Bianco, Remco Dijkman, Wim Nuijten, and Willem van Jaarsveld, propose a groundbreaking method that allows DRL to handle assignment problems with these previously problematic infinite state and action spaces.
Their work introduces three key contributions:
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The Assignment Graph: This is a novel graph-based way to represent assignment problems. Instead of trying to fit all information into a rigid vector, the assignment graph captures the relationships between resources, tasks, and potential assignments in a flexible, interconnected structure. This allows for dynamic changes in the number and attributes of tasks and resources.
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Mapping from Petri Nets: The paper provides a systematic way to translate process models, specifically a type of Petri Net called ‘Attributed Action-Evolution Petri Nets’, into these assignment graphs. This means that existing, widely recognized process modeling notations can be directly used to set up problems for DRL without extensive manual feature engineering. The process involves an ‘expansion’ step to ensure each part of the process is uniquely represented, followed by a ‘mapping’ to the graph structure.
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Adapted PPO Algorithm: To make DRL work with these dynamic graphs, the researchers adapted the Proximal Policy Optimization (PPO) algorithm, a popular DRL technique. This adaptation involves using specialized neural network layers, such as Heterogeneous Graph Attention Layers (HANConv), which are designed to process graph-structured data of varying sizes. It also addresses the challenge of a variable number of possible actions, ensuring the DRL agent can learn effectively even when the choices change from moment to moment.
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Empirical Validation
To demonstrate the effectiveness of their universal approach, the researchers tested it on three different types of assignment problems. These ranged from a simple problem with a small, finite state and action space, to a more complex one with a large but still finite space, and finally, to a problem with truly infinite state and action spaces (e.g., tasks with continuous budget values and dynamic arrival times).
The results were compelling. While all methods performed well on the simplest problem, the PPO algorithm trained with the new assignment graph representation (PPO Graph) significantly outperformed the traditional PPO using vector observations (PPO Vector) on the more complex finite problem. Crucially, for the problem with infinite state and action spaces, the PPO Graph method was able to learn close-to-optimal policies, whereas the vector-based approach simply could not represent the problem at all. This highlights the method’s ability to seamlessly handle problems that were previously intractable for DRL due to their dynamic and unbounded nature.
This research marks a significant step forward in applying Deep Reinforcement Learning to real-world business process optimization. By providing a flexible and universal way to represent dynamic task assignment problems, it opens doors for DRL to tackle a much broader range of complex scenarios. For more in-depth information, you can read the full research paper here.
