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The output of the search policy ψis a probability distri- |
bution over A, with ψj(x, o, B ;θ)the probability that grid |
cellj∈Ais selected by the policy ψ. |
In general, ψwill output a positive probability over all |
possible grid cells j∈A. However, in our setting there is |
no benefit to querying any grid cell j∈Athat has previ- |
ously been queried, i.e., for which o(j)≠0. Consequently, |
both at training (when the next decision is generated) and |
decision time, we restrict consideration only to j∈Awith |
o(j)=0, that is, which have yet to be queried, and sim- |
ply renormalize the output probabilities of ψ. Formally, we |
define ψ′ |
j(x, o, B ;θ)=0forjwitho(j)≠0, and define |
ψ′ |
j(x, o, B ;θ)=ψj(x, o, B ;θ) |
∑k∈A∶o(k)=0ψk(x, o, B ;θ). |
Grid cells jare then samples from ψ′ |
jat each search step |
during training. At decision time, on the other hand, we |
choose the grid cell jwith the maximum value of ψ′ |
j. |
This approach allows us to simply train the policy networkψwithout concern about feasibility of particular grid cell |
choices at decision time. In addition, to ensure that the pol- |
icy is robust to search budget uncertainty, we use randomly |
generated budgets Cat training time for different task in- |
stances. In the case of query costs c(j, k)=1for all grid |
cells j, k, each episode has a fixed length C. In general, |
episodes have no fixed length, and end whenever we ex- |
haust the total cost budget C. The overview of our proposed |
VAS framework is depicted in Figure 2. |
Next, we detail the proposed policy network architec- |
ture, and subsequently describe an adaptation of our ap- |
proach when instances at decision time follow a different |
distribution from those in the training data D, that is, the |
test-time adaptation (TTA) setting. |
4.1. Policy Network Architecture |
As shown in Figure 3, the policy network ψ(x, o, B ;θ)is |
composed of two components: 1) the image feature extrac- |
tion component f(x;ϕ)which maps the aerial image xto a |
low-dimensional latent feature representation z, and 2) the |
grid selection component g(z, o, B ;ζ), which combines the |
latent image representation zwith outcome of past search |
queries oand remaining budget Bto produce a probability |
distribution over grid cells to search in the next time step. |
Thus, the joint parameters of ψareθ=(ϕ, ζ). |
We use a frozen ResNet-34 [12], pretrained on Ima- |
geNet [16], as the feature extraction component f, followed |
by a1×1convolution layer. We combine this with the bud- |
getBand past query information oas follows. We apply |
the tiling operation in order to convert ointo a represen- |
tation with the same dimensions as the extracted features |
z=f(x), aiding us to effectively combine latent image |
feature and auxiliary state feature while preserving the grid |
specific spatial and query related information. Similarly, we |
apply tiling to the scalar budget Bto transform it to match |
the size of zand the tiled version of o. Finally, we concate- |
nate the features (z, o, B)along the channels dimension and |
pass them through the grid prediction network g. This con- |
sists of 1×1convolution to reduce dimensionality, flatten- |
ing, a small MLP with ReLU activations, and a final output |
(softmax) that represents the current grid probability. This |
4 |
yields the full policy network to be trained end to end via |
REINFORCE: ψ(x, o, B ;θ)=g(f(x;ϕ), o, B ;ζ). |
4.2. Test-Time Adaptation |
A central issue in our model, as in traditional active |
search, is that tasks faced at decision time may in some re- |
spects be novel, unlike tasks faced previously (e.g., repre- |
sented in the dataset D). We view this issue through the |
lens of test-time adaptation (TTA) , in which predictions are |
made on data that comes from a different distribution from |
training data. While a myriad of TTA techniques have been |
developed, they have focused almost exclusively on super- |
vised learning problems, rather than active search settings |
of the kind we study. Nevertheless, two common techniques |
can be either directly applied, or adapted, to our setting: 1) |
Test-Time Training (TTT) [27] and 2) FixMatch [26]. |
TTT makes use of a self-supervised objective at both |
training and prediction time by adding a self-supervised |
head ras a component of the policy model. The asso- |
ciated self-supervised loss (which is added during train- |
ing) is a quadratic reconstruction loss ∣∣x−r(z;η)∣∣, where |
z=f(x;ϕ)is the latent embedding of the input aerial image |
xandηthe parameters of r. At decision time, a new task |
image xis used to update policy parameters using just the |
reconstruction loss before we begin the search. Adaptation |
ofTTT to our V AS domain is therefore direct. |
The original variant of FixMatch uses pseudo-labels at |
decision time, which are predictions on weakly augmented |
variants of the input image x(keeping only those which are |
highly confident), to update model parameters. In our do- |
main, however, we can leverage the fact that we obtain ac- |
tual labels whenever we query regions of the image. We |
make use of this additional information as follows. When- |
ever a query jis successful (i.e., y(j)=1), we construct a |
label vector as the one-hot vector with a 1 in the location of |
the successful grid cell j. However if y(j)=0, we associate |
each queried grid cell with a 0, and assign uniform proba- |
bility distribution over all unqueried grids. We then update |
model parameters using a cross-entropy loss. |
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