We study unbiased (1+1) evolutionary algorithms on linear functions with an unknown number n of bits with non-zero weight. Static algorithms achieve an optimal runtime of O(n(ln n) 2+ε ), however, it remained unclear whether more dynamic parameter policies could yield better runtime guarantees. We consider two setups: one where the mutation rate follows a fixed schedule, and one where it may be adapted depending on the history of the run. For the first setup, we give a schedule that achieves a runtime of (1±o(1))βn ln n, where β ≈ 3.552, which is an asymptotic improvement over the runtime of the static setup. Moreover, we show that no schedule admits a better runtime guarantee and that the optimal schedule is essentially unique. For the second setup, we show that the runtime can be further improved to (1±o(1))en ln n, which matches the performance of algorithms that know n in advance.Finally, we study the related model of initial segment uncertainty with static position-dependent mutation rates, and derive asymptotically optimal lower bounds. This answers a question by Doerr, Doerr, and Kötzing.
In recent years, model-free methods that use deep learning have achieved great success in many different reinforcement learning environments. Most successful approaches focus on solving a single task, while multi-task reinforcement learning remains an open problem. In this paper, we present a model based approach to deep reinforcement learning which we use to solve different tasks simultaneously. We show that our approach not only does not degrade but actually benefits from learning multiple tasks. For our model, we also present a new kind of recurrent neural network inspired by residual networks that decouples memory from computation allowing to model complex environments that do not require lots of memory.
Inspired by the great success of unsupervised learning in Computer Vision and Natural Language Processing, the Reinforcement Learning community has recently started to focus more on unsupervised discovery of skills. Most current approaches, like DIAYN or DADS, optimize some form of mutual information objective. We propose a different approach that uses reward functions encoded by neural networks. These are trained iteratively to reward more complex behavior. In high-dimensional robotic environments our approach learns a wide range of interesting skills including front-flips for HALF-CHEETAH and onelegged running for HUMANOID. In the pixel-based Montezuma's Revenge environment our method also works with minimal changes and it learns complex skills that involve interacting with items and visiting diverse locations. A web version of this paper which shows animations for the different skills is available in https://as.inf.ethz.ch/research/open_ended_RL/main.html * Equal contribution.
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