A Markov decision process can be parameterized by a transition kernel and a reward function. Both play essential roles in the study of reinforcement learning as evidenced by their presence in the Bellman equations. In our inquiry of various kinds of ``costs'' associated with reinforcement learning inspired by the demands in robotic applications, rewards are central to understanding the structure of a Markov decision process and reward-centric notions can elucidate important concepts in reinforcement learning. Specifically, we studied the sample complexity of policy evaluation and developed a novel estimator with an instance-specific error bound of $\tilde{O}(\sqrt{\frac{\tau_s}{n}})$ for estimating a single state value. Under the online regret minimization setting, we refined the transition-based MDP constant, diameter, into a reward-based constant, maximum expected hitting cost, and with it, provided a theoretical explanation for how a well-known technique, potential-based reward shaping, could accelerate learning with expert knowledge. In an attempt to study safe reinforcement learning, we modeled hazardous environments with irrecoverability and proposed a quantitative notion of safe learning via reset efficiency. In this setting, we modified a classic algorithm to account for resets achieving promising preliminary numerical results. Lastly, for MDPs with multiple reward functions, we developed a planning algorithm that computationally efficiently finds Pareto optimal stochastic policies.

马尔可夫决策过程在强化学习中起着关键作用，本研究探讨了多种与强化学习相关的'成本'，研究了策略评估的样本复杂度，并开发了一种具有实例特定误差界限的新估计器；在在线遗憾最小化设置下，通过引入基于奖励的常量和基于潜力的奖励塑形技术，提供了理论上的解释；提出了一种安全强化学习研究方法，建立了重置效率的量化概念；针对具有多个奖励函数的决策过程，开发了一个能够计算出帕累托最优随机策略的规划算法。

关于马尔可夫决策过程的奖励结构