Paper:
Partially observable Markov decision processes (POMDPs) are a widely-used framework to model decision-making with uncertainty about the environment and under stochastic outcome. In conventional POMDP models, the observations that the agent receives originate from fixed known distribution. However, in a variety of real-world scenarios the agent has an active role in its perception by selecting which observations to receive. Due to combinatorial nature of such selection process, it is computationally intractable to integrate the perception decision with the planning decision. To prevent such expansion of the action space, we propose a greedy strategy for observation selection that aims to minimize the uncertainty in state. We develop a novel point-based value iteration algorithm that incorporates the greedy strategy to achieve near-optimal uncertainty reduction for sampled belief points. This in turn enables the solver to efficiently approximate the reachable subspace of belief simplex by essentially separating computations related to perception from planning. Lastly, we implement the proposed solver and demonstrate its performance and computational advantage in a range of robotic scenarios where the robot simultaneously performs active perception and planning.

Review:
This work addresses the problem of decomposing the observation acquisition from action planning in POMDPs.  Unfortunately, the paper has two major weaknesses.  First it is hindered by a confusing motivation, and the lack of clarity on the real purpose of the work is a problem throughout. Second the experiments are insufficient given current standards in the literature.
1. Motivation:  The introduction suggests that the main motivation is to reduce the computational cost of treating all observations within planning (“one must establish a trade-off between optimality and tractability”), though later, different reasons are offered (“power, processing capability, and cost constraints”).  It seems that each of these poses different constraints, and depending on which we are most concerned with, a different approximation scheme should be selected. For example, if the real concern is tractability of the POMDP solution, I don’t see why it’s not possible to just acquire all the sensor information, and afterwards decide how to approximate the tracking (this by the way is what most point-based POMDP methods effectively do).  For the proposed AP^2-POMDP, possibly a more reasonable motivation is high cost of observation acquisition; a clean argument would have to be made about the class of problems for which this constraint is crucial, why cardinality of sensor is the right way to articulate this constraint.
2. Experimental results:  The domains selected for the experiments are too simple, given current standards in the literature.  Looking at the 1D and 2D domains is fine to illustrate specific properties of your methods.  But it does not support the claim that the proposed model is more scalable than standard POMDPs.  In such simple domains, why not include results for a point-based method?  They should work in the 1D domain, probably also in the 2D domain.  Also, the setting for the 1-D domain, with a camera in every cell, seems very artificial.  First, if sensors are expensive, why put a camera in every cell?  And if they are not expensive, then why do we need to reason about which sensor to use at each step?  And why just read from k cameras at every step?  These questions point back to the concern regarding what is the real motivation for this work.  For the 2D domain, there are not even quantitative results on cumulative reward.  To be convincing, the results would need to be on substantially more complex domains; there are several POMDP benchmarks that could be considered, e.g. those in the work of Kurniawati et al.
Other comments:
-	Assumption 1 states that the observations from sensors are mutually independent give the state and action.  Can you explain why this is reasonable?  Or whether this is a strong assumption (unlikely to be met in practice)?
-	Some of the bounds seem like they could be very loose in practice, even (in the worse case) worse than the default bound of (R_max-R_min)/(1-\gamma). For example in Thm 3, in the case where the L1 distance between the 2 beliefs is 2, this is worse than the default bound.  Did you check what is the bound for the domains in the experiments?  Is it tighter than this?
-	A key statement is on p.8: “this added complexity is significantly lower than concatening the combinatorial perception actions with the planning actions”.   It is important to support this statement, ideally with both a precise complexity analysis, and with empirical results showing the lesser performance of standard point-based methods.
Minor comment:
-	The referencing style is broken and should be fixed, in particular proper use of Author (year) in the text.
-	The derivations in the top part of p.4 (Eqn 2-4 & surrounding text) are confusing, given that these apply to a standard POMDP, whereas on the previous page your present the AP^2-POMDP model. It might be better in Sec.2 to first (briefly) introduce POMDPs, with Eqn 2-4, then introduce AP^2-POMDP in Sec.3.
-	P.5: “It is worth noting that the objective function does not explicitly depend on perception actions”. This is a confusing statement; V depends on observations through b_t.  The next sentence clarifies this, but it would be better to avoid the confusing statement.
-	Alg.2:  Add a reference beside the title (unless you claim it is new).  Maybe Pineau et al. 2003.
-	P.7: “can be combined with any sampling and pruning method in other solvers” -> Add references for such sampling & pruning methods.