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While multitask representation learning has become a popular approach inreinforcement learning (RL) to boost the sample efficiency, the theoreticalunderstanding of why and how it works is still limited. Most previousanalytical works could only assume that the representation function is alreadyknown to the agent or from linear function class, since analyzing generalfunction class representation encounters non-trivial technical obstacles suchas generalization guarantee, formulation of confidence bound in abstractfunction space, etc. However, linear-case analysis heavily relies on theparticularity of linear function class, while real-world practice usuallyadopts general non-linear representation functions like neural networks. Thissignificantly reduces its applicability. In this work, we extend the analysisto general function class representations. Specifically, we consider an agentplaying $M$ contextual bandits (or MDPs) concurrently and extracting a sharedrepresentation function $\phi$ from a specific function class $\Phi$ using ourproposed Generalized Functional Upper Confidence Bound algorithm (GFUCB). Wetheoretically validate the benefit of multitask representation learning withingeneral function class for bandits and linear MDP for the first time. Lastly,we conduct experiments to demonstrate the effectiveness of our algorithm withneural net representation.

Provable General Function Class Representation Learning in Multitask Bandits and MDPs