Meta-learning the mirror map in policy mirror descent

Policy Mirror Descent (PMD) is a popular framework in reinforcement learning, serving as a unifying perspective that encompasses numerous algorithms. These algorithms are derived through the selection of a mirror map and enjoy finite-time convergence guarantees. Despite its popularity, the exploration of PMD's full potential is limited, with the majority of research focusing on a particular mirror map -- namely, the negative entropy -- which gives rise to the renowned Natural Policy Gradient (NPG) method. It remains uncertain from existing theoretical studies whether the choice of mirror map significantly influences PMD's efficacy. In our work, we conduct empirical investigations to show that the conventional mirror map choice (NPG) often yields less-than-optimal outcomes across several standard benchmark environments. By applying a meta-learning approach, we identify more efficient mirror maps that enhance performance, both on average and in terms of best performance achieved along the training trajectory. We analyze the characteristics of these learned mirror maps and reveal shared traits among certain settings. Our results suggest that mirror maps have the potential to be adaptable across various environments, raising questions about how to best match a mirror map to an environment's structure and characteristics.

Arbitrary Order Meta-Learning with Simple Population-Based Evolution

Meta-learning, the notion of learning to learn, enables learning systems to quickly and flexibly solve new tasks. This usually involves defining a set of outer-loop meta-parameters that are then used to update a set of inner-loop parameters. Most meta-learning approaches use complicated and computationally expensive bi-level optimisation schemes to update these meta-parameters. Ideally, systems should perform multiple orders of meta-learning, i.e. to learn to learn to learn and so on, to accelerate their own learning. Unfortunately, standard meta-learning techniques are often inappropriate for these higher-order meta-parameters because the meta-optimisation procedure becomes too complicated or unstable. Inspired by the higher-order meta-learning we observe in real-world evolution, we show that using simple population-based evolution implicitly optimises for arbitrarily-high order meta-parameters. First, we theoretically prove and empirically show that population-based evolution implicitly optimises meta-parameters of arbitrarily-high order in a simple setting. We then introduce a minimal self-referential parameterisation, which in principle enables arbitrary-order meta-learning. Finally, we show that higher-order meta-learning improves performance on time series forecasting tasks.