Recent studies on online reinforcement learning (RL) have demonstrated the
advantages of learning multiple behaviors from a single task, as in the case of
few-shot adaptation to a new environment. Although this approach is expected to
yield similar benefits in offline RL, appropriate methods for learning multiple
solutions have not been fully investigated in previous studies. In this study,
we therefore addressed the problem of finding multiple solutions from a single
task in offline RL. We propose algorithms that can learn multiple solutions in
offline RL, and empirically investigate their performance. Our experimental
results show that the proposed algorithm learns multiple qualitatively and
quantitatively distinctive solutions in offline RL.

通过研究在线强化学习，在少样本适应新环境的情况下，从一个任务中学习多种行为的优势已经被证明。然而，在离线强化学习中，学习多个解决方案的适当方法并未在先前研究中得到充分探讨。本研究因此解决了在离线强化学习中从单个任务中找到多个解决方案的问题。我们提出了一些可以在离线强化学习中学习多个解决方案的算法，并通过实证研究了它们的性能。实验结果表明，所提出的算法在离线强化学习中学习到了多个在质量和数量上都有显著差异的解决方案。

离线强化学习中从单个任务中发现多个解决方案

Discovering Multiple Solutions from a Single Task in Offline  Reinforcement Learning

Solving nonlinear partial differential equations (PDEs) with multiple
solutions using neural networks has found widespread applications in various
fields such as physics, biology, and engineering. However, classical neural
network methods for solving nonlinear PDEs, such as Physics-Informed Neural
Networks (PINN), Deep Ritz methods, and DeepONet, often encounter challenges
when confronted with the presence of multiple solutions inherent in the
nonlinear problem. These methods may encounter ill-posedness issues. In this
paper, we propose a novel approach called the Newton Informed Neural Operator,
which builds upon existing neural network techniques to tackle nonlinearities.
Our method combines classical Newton methods, addressing well-posed problems,
and efficiently learns multiple solutions in a single learning process while
requiring fewer supervised data points compared to existing neural network
methods.

通过结合经典的牛顿方法和现有神经网络技术，我们提出了一种名为牛顿信息神经算子的新方法，用于解决非线性偏微分方程（PDE），特别是存在多个解的问题，并且相对于现有的神经网络方法，我们的方法在单一学习过程中有效地学习了多个解，同时仅需要较少的监督数据点。