Self-Configurable Mesh-Networks for Scalable Distributed Submodular Bandit Optimization

TL;DR

The Value of Coordination (VoC), an information-theoretic metric that quantifies for each agent the benefit of information access to its neighbors, is defined, an information-theoretic metric that quantifies for each agent the benefit of information access to its neighbors.

Abstract

We study how to scale distributed bandit submodular coordination under realistic communication constraints in bandwidth, data rate, and connectivity. We are motivated by multi-agent tasks of active situational awareness in unknown, partially-observable, and resource-limited environments, where the agents must coordinate through agent-to-agent communication. Our approach enables scalability by (i) limiting information relays to only one-hop communication and (ii) keeping inter-agent messages small, having each agent transmit only its own action information. Despite these information-access restrictions, our approach enables near-optimal action coordination by optimizing the agents' communication neighborhoods over time, through distributed online bandit optimization, subject to the agents' bandwidth constraints. Particularly, our approach enjoys an anytime suboptimality bound that is also strictly positive for arbitrary network topologies, even disconnected. To prove the bound, we define the Value of Coordination (VoC), an information-theoretic metric that quantifies for each agent the benefit of information access to its neighbors. We validate in simulations the scalability and near-optimality of our approach: it is observed to converge faster, outperform benchmarks for bandit submodular coordination, and can even outperform benchmarks that are privileged with a priori knowledge of the environment.

Figures (9)

• Figure 1: Information Access Matters: A Multi-Camera Area Monitoring Example. Consider a multi-camera area monitoring task where four cameras must coordinate their fields of view (FOVs) via distributed communication to maximize total coverage. As shown in (a), suppose that cameras 1--3 have already fixed their FOVs (soft orange), and camera 4 must select its FOV from three predefined options (dark red). While the optimal choice for camera 4 depends on the FOVs of all other three, its communication bandwidth allows it to receive information from at most two of them at any current time. The three possible communication neighborhood configurations and the corresponding FOV selections are demonstrated in (b)--(d), among which the design in (c) yields the highest coverage and therefore the optimal FOV decision. This example illustrates that intelligent information access—enabled by active neighborhood design (possibly over multiple time steps)—can optimize action coordination performance in distributed settings with limited communication resources.
• Figure 2: Asymptotic approximation bounds of Anaconda. As $T\rightarrow\infty$, the bounds provided by \ref{['th:main', 'th:posteriori', 'th:asymptotic']} are shown with varying ranges of $\kappa_f$ and achieved $\beta$ (defined in \ref{['eq:beta']}). The a priori bound (red) varies with the sum of all agents' VoC; the a posteriori bound (orange) decreases as $\beta$ increases; and the combined bound (green) takes the maximum of the a priori lower bound and the a posteriori bound.
• Figure 3: Comparison of neighbor selection strategies with varying network density. Across 20 MC trials each with 2000 decision rounds, we compare NeiSel with two benchmark strategies, Nearest Neighbors and Random Neighbors. We tune the network density by varying the map area while fixing the network size at 20 agents: as the camera density grows, the network becomes sparser.
• Figure 4: Comparison of neighbor selection strategies in a structured environment. Three algorithms are compared with the same action selection strategy ActSel but different neighbor selection strategies ( NeiSel vs. nearest neighbors vs. random neighbors) in the same structured environment.
• Figure 5: Comparison of Anaconda, DFS-SG, and DFS-BSG for area monitoring without computation and communication delays. Cameras select their FOV directions using Anaconda with maximum communication neighborhood sizes in $\{0,\dots, 5\}$, or using DFS-SG or DFS-BSG. From (a) to (d), the communication range $c_i$ for all cameras $i\in{\cal N}$ increases from 10 to 16 to 20 to 80, and thus expanding each camera's coordination neighborhood ${\cal M}_i$ growing from a small locality to the full set ${\cal N}\setminus{i}$. DFS-SG is executed for a single decision round, whereas the other algorithms are run for 4000 rounds. Results are averaged over 20 Monte Carlo trials.

Theorems & Definitions (21)

• Definition 1: Normalized and Non-Decreasing Submodular Set Function fisher1978analysis
• Definition 2: 2nd-order Submodular Set Function crama1989characterizationfoldes2005submodularity
• Definition 3: Value of Coordination ( VoC)
• Definition 4: Curvature conforti1984submodular
• Proposition 1: Approximation Performance of ActSel
• Lemma 1: Monotonicity and Submodularity of VoC
• Definition 5: Static Regret of Action Selection
• Definition 6: $\rho(\kappa_{I,i}, \alpha_i)$-Approximate Static Regret of Neighbor Selection
• Lemma 2: Suboptimality Guarantee of ActSel
• Lemma 3: Suboptimality Guarantee of NeiSel