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Multi-goal reaching is an important problem in reinforcement learning neededto achieve algorithmic generalization. Despite recent advances in this field,current algorithms suffer from three major challenges: high sample complexity,learning only a single way of reaching the goals, and difficulties in solvingcomplex motion planning tasks. In order to address these limitations, weintroduce the concept of cumulative accessibility functions, which measure thereachability of a goal from a given state within a specified horizon. We showthat these functions obey a recurrence relation, which enables learning fromoffline interactions. We also prove that optimal cumulative accessibilityfunctions are monotonic in the planning horizon. Additionally, our method cantrade off speed and reliability in goal-reaching by suggesting multiple pathsto a single goal depending on the provided horizon. We evaluate our approach ona set of multi-goal discrete and continuous control tasks. We show that ourmethod outperforms state-of-the-art goal-reaching algorithms in success rate,sample complexity, and path optimality. Our code is available athttps://github.com/layer6ai-labs/CAE, and additional visualizations can befound at https://sites.google.com/view/learning-cae/.

C-Learning: Horizon-Aware Cumulative Accessibility Estimation