.%20In%20the%20realm%20of%20theory%2C%20we%20prove%20that%20the%20new%20constraints%20provide%20lower%20bounds%20on%20the%20cost%20of%20plans%20that%20comply%20with%20observations.%20We%20also%20provide%20an%20extensive%20empirical%20evaluation%20to%20assess%20how%20the%20new%20constraints%20improve%20the%20quality%20of%20the%20solution%2C%20and%20we%20found%20that%20they%20are%20especially%20informed%20in%20deciding%20which%20goals%20are%20unlikely%20to%20be%20part%20of%20the%20solution.%20Our%20novel%20recognition%20approaches%20have%20two%20pivotal%20advantages:%20first%2C%20they%20employ%20new%20IP%2FLP%20constraints%20for%20efficiently%20recognizing%20goals%3B%20second%2C%20we%20show%20how%20the%20new%20IP%2FLP%20constraints%20can%20improve%20the%20recognition%20of%20goals%20under%20both%20partial%20and%20noisy%20observability.)
%20and%20time%20requirements%20are%20taken%20into%20account.%20On%20the%20one%20hand%2C%20it%20is%20more%20sample-efficient%20than%20standard%20Deep%20Q-Learning%2C%20and%20it%20is%20able%20to%20generalize%20better%20across%20levels.%20On%20the%20other%20hand%2C%20it%20reduces%20problem-solving%20time%20when%20compared%20with%20a%20state-of-the-art%20automated%20planner%2C%20at%20the%20expense%20of%20obtaining%20plans%20with%20only%209%25%20more%20actions.)
%2C%20a%20high-level%20policy%20specifies%20a%20subgoal%20for%20the%20low-level%20policy%20to%20reach.%20Effective%20HRL%20hinges%20on%20a%20suitable%20subgoal%20represen%20tation%20function%2C%20abstracting%20state%20space%20into%20latent%20subgoal%20space%20and%20inducing%20varied%20low-level%20behaviors.%20Existing%20methods%20adopt%20a%20subgoal%20representation%20that%20provides%20a%20deterministic%20mapping%20from%20state%20space%20to%20latent%20subgoal%20space.%20Instead%2C%20this%20paper%20utilizes%20Gaussian%20Processes%20(GPs)%20for%20the%20first%20probabilistic%20subgoal%20representation.%20Our%20method%20employs%20a%20GP%20prior%20on%20the%20latent%20subgoal%20space%20to%20learn%20a%20posterior%20distribution%20over%20the%20subgoal%20representation%20functions%20while%20exploiting%20the%20long-range%20correlation%20in%20the%20state%20space%20through%20learnable%20kernels.%20This%20enables%20an%20adaptive%20memory%20that%20integrates%20long-range%20subgoal%20information%20from%20prior%20planning%20steps%20allowing%20to%20cope%20with%20stochastic%20uncertainties.%20Furthermore%2C%20we%20propose%20a%20novel%20learning%20objective%20to%20facilitate%20the%20simultaneous%20learning%20of%20probabilistic%20subgoal%20representations%20and%20policies%20within%20a%20unified%20framework.%20In%20experiments%2C%20our%20approach%20outperforms%20state-of-the-art%20baselines%20in%20standard%20benchmarks%20but%20also%20in%20environments%20with%20stochastic%20elements%20and%20under%20diverse%20reward%20conditions.%20Additionally%2C%20our%20model%20shows%20promising%20capabilities%20in%20transferring%20low-level%20policies%20across%20different%20tasks.)
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