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  1. Humans tame the complexity of mathematical reasoning by developing hierarchies of abstractions. With proper abstractions, solutions to hard problems can be expressed concisely, thus making them more likely to be found. In this paper, we propose Learning Mathematical Abstractions (LEMMA): an algorithm that implements this idea for reinforcement learning agents in mathematical domains. LEMMA augments Expert Iteration with an abstraction step, where solutions found so far are revisited and rewritten in terms of new higher-level actions, which then become available to solve new problems. We evaluate LEMMA on two mathematical reasoning tasks--equation solving and fraction simplification--in a step-by-step fashion. In these two domains, LEMMA improves the ability of an existing agent, both solving more problems and generalizing more effectively to harder problems than those seen during training. 
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  2. Offline goal-conditioned reinforcement learning (GCRL) promises general-purpose skill learning in the form of reaching diverse goals from purely offline datasets. We propose Go al-conditioned f - A dvantage R egression (GoFAR), a novel regression-based offline GCRL algorithm derived from a state-occupancy matching perspective; the key intuition is that the goal-reaching task can be formulated as a state-occupancy matching problem between a dynamics-abiding imitator agent and an expert agent that directly teleports to the goal. In contrast to prior approaches, GoFAR does not require any hindsight relabeling and enjoys uninterleaved optimization for its value and policy networks. These distinct features confer GoFAR with much better offline performance and stability as well as statistical performance guarantee that is unattainable for prior methods. Furthermore, we demonstrate that GoFAR's training objectives can be re-purposed to learn an agent-independent goal-conditioned planner from purely offline source-domain data, which enables zero-shot transfer to new target domains. Through extensive experiments, we validate GoFAR's effectiveness in various problem settings and tasks, significantly outperforming prior state-of-art. Notably, on a real robotic dexterous manipulation task, while no other method makes meaningful progress, GoFAR acquires complex manipulation behavior that successfully accomplishes diverse goals. 
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