Our goal is to develop theory and algorithms for establishing fundamental
limits on performance for a given task imposed by a robot's sensors. In order
to achieve this, we define a quantity that captures the amount of task-relevant
information provided by a sensor. Using a novel version of the generalized Fano
inequality from information theory, we demonstrate that this quantity provides
an upper bound on the highest achievable expected reward for one-step decision
making tasks. We then extend this bound to multi-step problems via a dynamic
programming approach. We present algorithms for numerically computing the
resulting bounds, and demonstrate our approach on three examples: (i) the lava
problem from the literature on partially observable Markov decision processes,
(ii) an example with continuous state and observation spaces corresponding to a
robot catching a freely-falling object, and (iii) obstacle avoidance using a
depth sensor with non-Gaussian noise. We demonstrate the ability of our
approach to establish strong limits on achievable performance for these
problems by comparing our upper bounds with achievable lower bounds (computed
by synthesizing or learning concrete control policies).

发展机器人传感器性能极限的理论和算法，定义了一个获取任务相关信息的量，利用信息理论的广义 Fano 不等式，在一步决策任务和多步问题上提供性能上限的算法，并在三个实例中进行了演示。