Scaling of optimal RANDAO manipulation with epoch length ℓ

Determine whether the percentage improvement over the honest policy achieved by the optimal RANDAO manipulation strategy in the reduced Markov decision process M'_G scales with the epoch length ℓ in the manner indicated by the truncated evaluation plot for ℓ ∈ {16, 32, 64, 128}. Specifically, ascertain if the empirical scaling behavior shown in the figure “Percentage improvement over honest for ℓ ∈ {16,32,64,128}” accurately reflects the true dependence on ℓ despite floating‑point numerical instability in the evaluation for ℓ > 32.

Background

The paper extends its methodology beyond Ethereum’s current epoch length ℓ = 32 to explore how optimal RANDAO manipulation varies with different epoch lengths. For ℓ > 32, the authors note that numerical instability in 64‑bit floating‑point arithmetic affects the evaluation of a key probability expression, leading them to introduce a mitigation that truncates inner sums close to 1 to improve stability.

Using this mitigation, they present a plot of percentage improvement over the honest policy for ℓ ∈ {16, 32, 64, 128}. However, they caution that these extended results are not provably accurate due to the numerical instability, and explicitly conjecture that the observed plot is representative of the true scaling behavior with ℓ. This leaves open the task of rigorously confirming (or refuting) the conjectured scaling, potentially by analyzing numerical errors or devising provably stable evaluation methods for larger ℓ.

References

We conjecture that this plot is representative of how the results scale with ℓ, although unlike our main results the experiments are not provably accurate due to the aforementioned numerical instability. If one desires provable numerical guarantees on these quantities, one would need an analysis of numerical error induced by floating point representations of the machines that run the evaluation.

— Optimal RANDAO Manipulation in Ethereum  (2409.19883 - Alpturer et al., 2024) in Section “Considering ℓ ≠ 32” (label: sec:numeric)

Three directions remain open. First, \cref{sec:mitigation} analyzes a single tail-slashing curve built from a decaying penalty and a multi-miss multiplier. A natural extension is to explore alternative slashing curves, which may achieve smaller costs for honest validators under the same deterrence guarantee. Second, our framework works at the epoch level and we assume that the adversary commits to an action for the entire epoch at once. However, in practice, the adversary may do even better by adapting their strategy based on the blocks they see in the current epoch online. Analyzing this adaptive strategy is an interesting direction for future work. Third, the empirical gap between our upper and lower bounds is much smaller than our sample-complexity bound predicts, suggesting room for a tighter analysis.

— RANDAO Manipulation in the Presence of MEV  (2610.02143 - Alpturer et al., 1 Oct 2026) in Section 6, subparagraph “Future work”