Apprenticeship learning with prior beliefs using inverse optimization
This work addresses apprenticeship learning for robotics or AI systems by integrating prior knowledge, though it is incremental as it builds on existing inverse optimization and convex-analytic frameworks.
The authors tackled the problem of apprenticeship learning with suboptimal experts by incorporating prior beliefs on cost functions into inverse reinforcement learning, formulating it as a regularized min-max problem and solving it with stochastic mirror descent to improve learning of cost vectors and policies.
The relationship between inverse reinforcement learning (IRL) and inverse optimization (IO) for Markov decision processes (MDPs) has been relatively underexplored in the literature, despite addressing the same problem. In this work, we revisit the relationship between the IO framework for MDPs, IRL, and apprenticeship learning (AL). We incorporate prior beliefs on the structure of the cost function into the IRL and AL problems, and demonstrate that the convex-analytic view of the AL formalism (Kamoutsi et al., 2021) emerges as a relaxation of our framework. Notably, the AL formalism is a special case in our framework when the regularization term is absent. Focusing on the suboptimal expert setting, we formulate the AL problem as a regularized min-max problem. The regularizer plays a key role in addressing the ill-posedness of IRL by guiding the search for plausible cost functions. To solve the resulting regularized-convex-concave-min-max problem, we use stochastic mirror descent (SMD) and establish convergence bounds for the proposed method. Numerical experiments highlight the critical role of regularization in learning cost vectors and apprentice policies.