From Validator Selection to Portfolio Collection Optimization in Proof-of-Stake Blockchains
Authors: Jonas Gehrlein, Grzegorz Miebs, Matteo Brunelli, Adam Mielniczuk, Miłosz Kadziński
Organizations: Parity Technologies AG, Zug, Switzerland · Institute of Computing Science, Poznan University of Technology, Poznań, Poland · Department of Industrial Engineering, University of Trento, Italy
Abstract
We consider a problem arising in proof-of-stake blockchain environments, where agents called nominators select validators - entities responsible for maintaining the blockchain's physical infrastructure. The selection process is inherently subjective and multi-criterial and combines with the fact that nominators commonly operate through multiple accounts. This gives rise to a portfolio selection problem, where agents seek to distribute their nominations across accounts to diversify risk. We propose a decision support framework to optimize this selection by simultaneously maximizing two objectives: the expected utility of the validators likely to be allocated, representing portfolio quality and profitability, and the expected entropy of the allocation, representing diversification and risk mitigation across stashes. Validator utilities are derived using an original active preference learning procedure based on multi-attribute value theory, with emphasis on top-ranked validators. The resulting bi-objective optimization problem is solved with a multi-objective evolutionary algorithm and, to support the final choice, we introduce an interactive binary search navigation procedure that guides the nominator through the front and identifies a satisfactory trade-off with only a few questions. Numerical experiments examine the optimization strategies, while an expert assessment involving five experienced nominators confirms the approach's practical relevance and usefulness.
In black-box optimization, a central question is which algorithm to use to solve a given, previously unseen, problem. Selecting a single algorithm, however, entails inherent risks: inaccuracies in the selector may lead to poor choices, and even well-performing algorithms with high variance can yield unsatisfactory results in a single run. A natural remedy is to split the evaluation budget across multiple runs of potentially different algorithms. Such sequential algorithm portfolios benefit from variance reduction and complementarities between algorithms, often outperforming approaches that allocate the entire budget to a single solver. While effective portfolios can be constructed post-hoc, transferring this idea to the algorithm selection setting is non-trivial. We show that a naive portfolio constructed over the full training set already outperforms the strongest traditional baseline, the virtual best solver. We then propose a simple yet effective k-nearest-neighbor-based finetuning approach to construct portfolios tailored to unseen instances, yielding further improvements and highlighting the effectiveness of portfolio selection in fixed-budget black-box optimization.
Voting methods weighted by stakes are the fundamental governance paradigm in Proof-of-Stake (PoS) blockchains. Such a paradigm is known to be prone to power distortions: a few users possessing large stakes may completely control decision making, even without owning the totality of the stakes. We study this phenomenon through the lens of computational social choice, focusing on the extent of power imbalances in stake-weighted voting when power is quantified using the Penrose-Banzhaf power index. Our work presents both analytical and empirical contributions. Analytically, we demonstrate that while a perfect alignment between power and relative stake ownership is generally unattainable, it can be approximated in expectation under specific conditions. Empirically, using data from a real-world on-chain governance system (Project Catalyst), we provide a more fine-grained understanding of the power imbalances that are likely to occur in current stake-weighted governance systems.
The operation of blockchain is governed by consensus algorithms (CA). Several consensus mechanisms require significant computational power, while others necessitate high amounts of stakes to select the participant to validate and verify the transactions in the block, leading to centralisation of power and participant exclusion. This paper proposes a novel methodology to address these issues in reputation-based consensus algorithms by studying the reputation behaviour of the validator using intuitionistic fuzzy sets (IFSs) and uninorm aggregation operations (UAOs). Our approach uses IFSs to express the "reputation" because the reputation values in a consensus algorithm eventually imply uncertainty, and IFSs facilitate the representation of a lack of precise knowledge about reputation. Moreover, this methodology utilises uninorm aggregation operations to monitor reputation over time and reinforces the importance of negative and positive reputation. Consequently, this solution allows validators to rectify past failures in subsequent verification processes and foster an equitable consensus algorithm design. The proposed framework maintains linear computational complexity and does not introduce additional communication overhead beyond the underlying consensus protocol. Supported by experimental results, our methodology demonstrates improved performance and evaluation, promising advancements in blockchain network fairness and inclusivity.
Bruno Ramos-Cruz, Javier Andreu-Perez, David Richerby +1