Many real-life problems are complex due to their multi-objective nature. Over the past decade, there has been growing research on Multi-Objective Reinforcement Learning (MORL) problems, which simulate the complexities of real-life scenarios. Because there are multiple objectives to be optimized, the majority of the MORL methods focus on providing a dense set of solutions called the Pareto Front as a result. The issues with the current approaches are that generating a large solution set requires high computational costs, and it can still be difficult for the user to find their most preferred solutions from a large solution set. In this research, we propose an interactive MORL method where the user is asked for their preferred solution in every iteration from the current solution set, and the algorithm utilizes this information to enhance its learning process to find preference-aligned solutions. This is achieved by bounding the solution space to only search for new policies that outperform the previously user-selected solution within these bounds. We evaluate our method using an artificial user function to simulate preferences, comparing it with non-interactive MORL methods. Metrics to compare the quality of solutions include the number of learning steps required to converge to a preferred solution, the value achieved on the artificial user function. The results demonstrate that the interactive method provides a dense set of solutions in the user’s region of interest, and it tends to converge faster towards the user’s preferred solution.

Several algorithms can often be used to solve a complex problem, such as the SAT problem or the graph coloring problem. Those algorithms differ in terms of speed based on the size or other features of the problem. Some algorithms perform much faster on a small size while others perform noticeably better on a larger instance. The optimization problem in this case is to select the best-performing algorithm based on the problem features, resulting in a much faster overall runtime. This is defined as the algorithm selection problem. Many different approaches have been used to solve this problem, such as constructing optimal decision trees. However, there is little published data on using optimal decision trees for algorithm selection and one study reveals a problem in finding a feasible solution on a large number of problem instances. We provide new insights into solving algorithm selection using a dynamic programming approach. The motivation to use this novel approach is that recent studies suggest it has lower scalability issues compared to the traditional optimal decision tree algorithms, due to several efficient techniques such as caching and frequency counting method. The investigation has shown that compared to the integer programming method, the dynamic programming approach is significantly faster and is able to solve large problem instances.