  We introduce a new algorithm for multi-objective reinforcement learning
(MORL) with linear preferences, with the goal of enabling few-shot adaptation
to new tasks. In MORL, the aim is to learn policies over multiple competing
objectives whose relative importance (preferences) is unknown to the agent.
While this alleviates dependence on scalar reward design, the expected return
of a policy can change significantly with varying preferences, making it
challenging to learn a single model to produce optimal policies under different
preference conditions. We propose a generalized version of the Bellman equation
to learn a single parametric representation for optimal policies over the space
of all possible preferences. After an initial learning phase, our agent can
execute the optimal policy under any given preference, or automatically infer
an underlying preference with very few samples. Experiments across four
different domains demonstrate the effectiveness of our approach.
