The use of Potential Based Reward Shaping (PBRS) has shown great promise in
the ongoing research effort to tackle sample inefficiency in Reinforcement
Learning (RL). However, the choice of the potential function is critical for
this technique to be effective. Additionally, RL techniques are usually
constrained to use a finite horizon for computational limitations. This
introduces a bias when using PBRS, thus adding an additional layer of
complexity. In this paper, we leverage abstractions to automatically produce a
"good" potential function. We analyse the bias induced by finite horizons in
the context of PBRS producing novel insights. Finally, to asses sample
efficiency and performance impact, we evaluate our approach on four
environments including a goal-oriented navigation task and three Arcade
Learning Environments (ALE) games demonstrating that we can reach the same
level of performance as CNN-based solutions with a simple fully-connected
network.

利用抽象技术在有限时间内生成 “好” 的潜力函数，分析在 Potential Based Reward Shaping 中有限时间引入的偏差，并在四个不同环境中进行评估，证明我们可以通过简单的全连接网络达到与基于 CNN 的解决方案相同的性能水平。

强化学习中抽象和基于潜力的奖励塑形的样本效率研究

On the Sample Efficiency of Abstractions and Potential-Based Reward  Shaping in Reinforcement Learning

We consider restless multi-armed bandit (RMAB) with a finite horizon and
multiple pulls per period. Leveraging the Lagrangian relaxation, we approximate
the problem with a collection of single arm problems. We then propose an
index-based policy that uses optimal solutions of the single arm problems to
index individual arms, and offer a proof that it is asymptotically optimal as
the number of arms tends to infinity. We also use simulation to show that this
index-based policy performs better than the state-of-art heuristics in various
problem settings.

该研究提出了一种基于拉格朗日松弛法的单臂问题集合的无休止多臂赌博机指数策略，利用模拟证明其表现优于现有启发式方法。

有限时间内动态赌博机渐近最优指数策略

An Asymptotically Optimal Index Policy for Finite-Horizon Restless  Bandits

We consider impulse control problems in finite horizon for diffusions with
decision lag and execution delay. The new feature is that our general framework
deals with the important case when several consecutive orders may be decided
before the effective execution of the first one. This is motivated by financial
applications in the trading of illiquid assets such as hedge funds. We show
that the value functions for such control problems satisfy a suitable version
of dynamic programming principle in finite dimension, which takes into account
the past dependence of state process through the pending orders. The
corresponding Bellman partial differential equations (PDE) system is derived,
and exhibit some peculiarities on the coupled equations, domains and boundary
conditions. We prove a unique characterization of the value functions to this
nonstandard PDE system by means of viscosity solutions. We then provide an
algorithm to find the value functions and the optimal control. This easily
implementable algorithm involves backward and forward iterations on the domains
and the value functions, which appear in turn as original arguments in the
proofs for the boundary conditions and uniqueness results.

本文研究了带决策滞后和执行延迟的扩散情况下的脉冲控制问题。我们在动态规划原理的适当版本下，通过挂起的订单考虑状态过程的过去依赖关系，导出对应的 Bellman 偏微分方程系统，并通过粘性解的方式得出了对该非标准 PDE 系统的价值函数唯一刻画和计算最优控制的算法。