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   We present a policy gradient method for Multi-Objective Reinforcement Learning under unknown, linear preferences. By enforcing Pareto stationarity, a first-order condition for Pareto optimality, we are able to design a simple policy gradient al- gorithm that approximates the Pareto front and infers the unknown preferences. Our method relies on a projected gradient descent solver that identifies common ascent directions for all objectives. Leveraging the solution of that solver, we in- troduce Pareto Policy Adaptation (PPA), a loss function that adapts the policy to be optimal with respect to any distribution over preferences. PPA uses implicit differentiation to back-propagate the loss gradient bypassing the operations of the projected gradient descent solver. Our approach is straightforward, easy to imple- ment and can be used with all existing policy gradient and actor-critic methods. We evaluate our method in a series of reinforcement learning tasks. 

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2. Pareto Policy Adaptation

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   We present a policy gradient method for Multi-Objective Reinforcement Learning under unknown, linear preferences. By enforcing Pareto stationarity, a first-order condition for Pareto optimality, we are able to design a simple policy gradient algorithm that approximates the Pareto front and infers the unknown preferences. Our method relies on a projected gradient descent solver that identifies common ascent directions for all objectives. Leveraging the solution of that solver, we introduce Pareto Policy Adaptation (PPA), a loss function that adapts the policy to be optimal with respect to any distribution over preferences. PPA uses implicit differentiation to back-propagate the loss gradient bypassing the operations of the projected gradient descent solver. Our approach is straightforward, easy to implement and can be used with all existing policy gradient and actor-critic methods. We evaluate our method in a series of reinforcement learning tasks 

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   https://doi.org/10.1098/rspb.2018.2727  

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