利用次模价值函数扩展主动感知
Exploiting Submodular Value Functions For Scaling Up Active Perception
摘要：
在主动感知任务中，智能体的目标是选择感官动作，以减少其对一个或多个隐藏变量的不确定性。虽然部分可观察马尔可夫决策过程（POMDP）提供了一个自然的模型，这样的问题，奖励功能，直接惩罚代理的信念的不确定性，可以删除分段线性和凸属性的价值函数所需的大多数POMDP规划。此外，随着代理可用的传感器数量的增加，POMDP规划的计算成本也随之呈指数级增长，使得POMDP规划不可行。在这篇文章中，我们解决了建模和规划主动感知任务的双重挑战。我们展示了$ρ$ POMDP和POMDP-IR的数学等价性，这两个框架用于建模主动感知任务，恢复了价值函数的PWLC属性。为了有效地规划主动感知任务，我们识别和利用POMDP-IR的独立性，以减少求解POMDP-IR（和$ρ$ POMDP）的计算成本。我们提出了贪婪的基于点的值迭代（PBVI），一个新的POMDP规划方法，使用贪婪的最大化，大大提高了可扩展性的行动空间的主动感知POMDP。此外，我们表明，在一定的条件下，包括子模块，使用贪婪PBVI计算的价值函数保证有界误差的最佳价值函数。我们建立的条件下，价值函数的主动感知POMDP保证是次模。最后，我们提出了一个详细的实证分析，从多摄像机跟踪系统在一个购物中心收集的数据集。我们的方法实现了类似的性能，现有的方法，但在一小部分的计算成本，导致更好的可扩展性解决主动感知任务。
英文摘要：
In active perception tasks, an agent aims to select sensory actions that reduce its uncertainty about one or more hidden variables. While partially observable Markov decision processes (POMDPs) provide a natural model for such problems, reward functions that directly penalize uncertainty in the agent's belief can remove the piecewise-linear and convex property of the value function required by most POMDP planners. Furthermore, as the number of sensors available to the agent grows, the computational cost of POMDP planning grows exponentially with it, making POMDP planning infeasible with traditional methods. In this article, we address a twofold challenge of modeling and planning for active perception tasks. We show the mathematical equivalence of $ρ$POMDP and POMDP-IR, two frameworks for modeling active perception tasks, that restore the PWLC property of the value function. To efficiently plan for active perception tasks, we identify and exploit the independence properties of POMDP-IR to reduce the computational cost of solving POMDP-IR (and $ρ$POMDP). We propose greedy point-based value iteration (PBVI), a new POMDP planning method that uses greedy maximization to greatly improve scalability in the action space of an active perception POMDP. Furthermore, we show that, under certain conditions, including submodularity, the value function computed using greedy PBVI is guaranteed to have bounded error with respect to the optimal value function. We establish the conditions under which the value function of an active perception POMDP is guaranteed to be submodular. Finally, we present a detailed empirical analysis on a dataset collected from a multi-camera tracking system employed in a shopping mall. Our method achieves similar performance to existing methods but at a fraction of the computational cost leading to better scalability for solving active perception tasks.
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