Delphi: Efficient Asynchronous Approximate Agreement for Distributed Oracles

TL;DR

Delphi addresses asynchronous distributed consensus among $n$ nodes with Byzantine faults while enforcing convex validity, targeting real-world sensor/oracle networks. It replaces expensive common-coin or heavy-round schemes with a deterministic, multi-level, checkpoint-based BinAA framework and a weighted averaging technique that yields $\tilde{O}(n^2)$ communication per round and low computation. By tying BinAA outputs across many checkpoints with level-wise weights and pruning contributions from distant levels, Delphi achieves $\epsilon$-agreement and $\rho$-relaxed validity under thin-tailed input distributions, with termination guarantees. Empirically, Delphi delivers substantial latency and bandwidth improvements over prior state-of-the-art protocols in both CPS and cloud environments (e.g., up to $8\times$ faster in CPS and $3\times$ in AWS for $n=160$), enabling practical deployment in distributed oracle networks and cyber-physical systems.

Abstract

Agreement protocols are crucial in various emerging applications, spanning from distributed (blockchains) oracles to fault-tolerant cyber-physical systems. In scenarios where sensor/oracle nodes measure a common source, maintaining output within the convex range of correct inputs, known as convex validity, is imperative. Present asynchronous convex agreement protocols employ either randomization, incurring substantial computation overhead, or approximate agreement techniques, leading to high $\mathcal{\tilde{O}}(n^3)$ communication for an $n$-node system. This paper introduces Delphi, a deterministic protocol with $\mathcal{\tilde{O}}(n^2)$ communication and minimal computation overhead. Delphi assumes that honest inputs are bounded, except with negligible probability, and integrates agreement primitives from literature with a novel weighted averaging technique. Experimental results highlight Delphi's superior performance, showcasing a significantly lower latency compared to state-of-the-art protocols. Specifically, for an $n=160$-node system, Delphi achieves an 8x and 3x improvement in latency within CPS and AWS environments, respectively.

Figures (7)

• Figure 1: Description of symbols used in Delphi
• Figure 2: Delphi with one level: The flags denote the checkpoints, and antennae denote honest inputs. Green checkpoints have weight $w_{k\xspace}^{}\xspace=1$ and drive agreement among nodes, and red checkpoints are outside the range of honest inputs that can have a non-zero weight and contribute to Validity relaxation. When $\delta\xspace_2>\rho_{}\xspace$, no green checkpoint exists, which results in agreement failure. A higher $2\rho_{}\xspace$ enables nodes to reach agreement with range $\delta\xspace_2$, but also adds the weight of farther red checkpoints when the range is $\delta\xspace_1$, which affects Validity negatively.
• Figure 3: Delphi with multiple levels: As $\delta\xspace{}<2\rho_{}\xspace$, all levels $l\geq2$ have at least one green flag, which implies $w_{l}\xspace=\max_{k}w_{k\xspace}^{}\xspace$ is 1 for levels 2,3,4. We eliminate contributions of levels 3 and 4 by using weight $w'_{l}\xspace=w_{l}\xspace|w_{l}\xspace-w_{l-1}\xspace|$ in the weighted average.
• Figure 4: Bitcoin price range histogram: We plot a histogram of observed $\delta\xspace = |\max(V_{\mathsf{h}}\xspace)-\min(V_{\mathsf{h}}\xspace)|$ in US Dollars on the x-axis and the number of times the $\delta$ values in the bin appeared in the two weeks on the y-axis. We also fit different probability distributions and observe that Fréchet and Gumbel distributions, the two distributions used to model extreme order values, are the closest fit, with Fréchet being the better fit.
• Figure 5: IoU histogram for Drone-based object detection: We plot the IoU values of detections output by the detection program and analyze their incidence by bucketing them into bins. These values follow a Gamma distribution, which has a thin tail.

Theorems & Definitions (10)

• Definition 2.1
• Definition 2.2
• Theorem 4.1
• proof
• Lemma 4.2
• proof
• Theorem 4.3
• proof
• Theorem 4.4
• proof