Sensor Selection via GFlowNets: A Deep Generative Modeling Framework to Navigate Combinatorial Complexity

TL;DR

This work tackles the combinatorial challenge of selecting a fixed-size sensor subset from a large pool to optimize a QoS metric under cost considerations. It introduces Generative Flow Networks (GFlowNets) as an unsupervised, criterion-agnostic framework that treats subset selection as a deterministic MDP and learns a flow-based policy to sample subsets with probability proportional to their reward, enabling efficient exploration of massive solution spaces. The authors demonstrate that GFLOW-SS outperforms traditional convex relaxations and greedy methods on linear estimation tasks, and extend the framework to ISAC via MOGFLOW-SS, which balances radar CRB and communication rate with strong generalization to unseen preference vectors. This approach provides a scalable, flexible tool for sensor and ISAC design, reducing reliance on annotated data and enabling robust multiobjective trade-offs across diverse operational regimes.

Abstract

The performance of sensor arrays in sensing and wireless communications improves with more elements, but this comes at the cost of increased energy consumption and hardware expense. This work addresses the challenge of selecting $k$ sensor elements from a set of $m$ to optimize a generic Quality-of-Service metric. Evaluating all $\binom{m}{k}$ possible sensor subsets is impractical, leading to prior solutions using convex relaxations, greedy algorithms, and supervised learning approaches. The current paper proposes a new framework that employs deep generative modeling, treating sensor selection as a deterministic Markov Decision Process where sensor subsets of size $k$ arise as terminal states. Generative Flow Networks (GFlowNets) are employed to model an action distribution conditioned on the state. Sampling actions from the aforementioned distribution ensures that the probability of arriving at a terminal state is proportional to the performance of the corresponding subset. Applied to a standard sensor selection scenario, the developed approach outperforms popular methods which are based on convex optimization and greedy algorithms. Finally, a multiobjective formulation of the proposed approach is adopted and applied on the sparse antenna array design for Integrated Sensing and Communication (ISAC) systems. The multiobjective variation is shown to perform well in managing the trade-off between radar and communication performance.

Figures (8)

• Figure 1: The Sensor Selection MDP pertains to the task of selecting 2 sensor elements from a total of 3. In the visual representation, the red circles signify active elements, while the white circles indicate inactive elements.
• Figure 2: Comparison of the performance of GFLOW-SS, GREEDY-SS and CVX-OPT-SS for the problem of selecting $k$ sensors out of $100$. The parameter $k$ ranges from $5$ to $15$. Each point corresponds to the average performance of the respective approach over $8$ different instantiations. The GFLOW-SS approach is trained for $40000$ root-to-leaf MDP trajectories for every instantiation of the problem. This corresponds to $40000 \times k$ gradient descent steps.
• Figure 3: Comparison of the performance of GFLOW-SS (both for the best and the $2$nd best subset), GREEDY-SS and CVX-OPT-SS for the problem of selecting $k$ sensors out of $50$. The parameter $k$ ranges from $10$ to $15$. Each point corresponds to the average performance of the respective approach over $8$ different instantiations. In order to select the $2$nd best subset, the action that corresponds to the $2$nd best flow is chosen at each state. The GFLOW-SS approach is trained for $40000$ root-to-leaf MDP trajectories for every instantiation of the problem. This corresponds to $40000 \times k$ gradient descent steps.
• Figure 4: The architecture of the two parametrizations ($Z_{\mathbf{w}}(\boldsymbol{\beta})$, $P_{\mathbf{w}}^{F} (\cdot| \mathbf{s}; \boldsymbol{\beta})$) employed for MOGFLOW-SS.
• Figure 5: The trajectory balance loss for MOGFLOW-SS is computed over $60000$ episodes, representing root-to-leaf trajectories.