Tarun Chitra

Muriel Médard, Tarun Chitra, Moritz Grundei et al.

We study pricing mechanisms for low-latency payload delivery in settings where participant rewards depend on the time required to reconstruct a payload. In such environments, the decoding time distribution determines deadline-meeting probabilities and therefore bounds a participant's willingness to pay for additional delivery rate. Using a mean-field formulation, we derive price-rate bounds from simple stochastic arrival models and instantiate them for (i) unsharded transmission and (ii) sharded delivery under three regimes: uncoded sharding, fixed-rate erasure coding, and rateless coding. These bounds yield a comparative characterization of how symbol usefulness translates into economic value under deadline-driven utilities. We further analyze a two-lane service consisting of a base lane and a Random Linear Network Coding (RLNC) fast lane. In this turbo decoding setting, a receiver combines shards arriving via both lanes to minimize time to decode. Under a fixed base-lane price-rate pair and an aggregate rate constraint, we derive a fast-lane pricing bound and show how even modest additional RLNC rate can generate measurable utility gains, depending on the base-lane propagation regime. The framework extends naturally to stepwise reward schedules with multiple deadlines, and we illustrate its applicability on representative scenarios motivated by blockchain message dissemination and latency-sensitive competition.

Tarun Chitra

Chain-of-thought reasoning enables large language models to solve multi-step tasks by framing problem solving as sequential decision problems. Outcome-based rewards, which provide feedback only on final answers, show impressive success, but face challenges with credit assignment and slow convergence. In contrast, procedure-based rewards offer efficient step-level feedback, but typically require costly human supervision. We introduce \emph{Backwards Adaptive Reward Shaping} (BARS), a no-regret framework that converts sparse outcomes-based rewards into effective procedure-based signals. BARS uses sparse rewards generated from terminal-state priors and cover trees to scale rewards while preventing exploitation. With Bellman contraction and $(Δ, ε)$-gap rewards, our backward Euler solver achieves $ε$-accuracy in $O\left((R_{\max}/Δ)\log(1/ε)\right)$ iterations with $O(\log T)$ dynamic regret over $T$ rounds. Our analysis, based on generic chaining, continuous scaling limits, and non-linear Feynman-Kac bounds, connects recent outcome-based methods' empirical successes with the benefits of intermediate supervision. Combined, this provides the first rigorous no-regret algorithm for outcome reward shaping, providing a theoretical foundation for the empirical success of DeepSeek's R1.

Alexandre Obadia, Alejo Salles, Lakshman Sankar et al.

The multi-chain future is upon us. Modular architectures are coming to maturity across the ecosystem to scale bandwidth and throughput of cryptocurrency. One example of such is the Ethereum modular architecture, with its beacon chain, its execution chain, its Layer 2s, and soon its shards. These can all be thought as separate blockchains, heavily inter-connected with one another, and together forming an ecosystem. In this work, we call each of these interconnected blockchains "domains", and study the manifestation of Maximal Extractable Value (MEV, a generalization of "Miner Extractable Value") across them. In other words, we investigate whether there exists extractable value that depends on the ordering of transactions in two or more domains jointly. We first recall the definitions of Extractable and Maximal Extractable Value, before introducing a definition of Cross-Domain Maximal Extractable Value. We find that Cross-Domain MEV can be used to measure the incentive for transaction sequencers in different domains to collude with one another, and study the scenarios in which there exists such an incentive. We end the work with a list of negative externalities that might arise from cross-domain MEV extraction and lay out several open questions. We note that the formalism in this work is a work in progress, and we hope that it can serve as the basis for formal analysis tools in the style of those presented in Clockwork Finance, as well as for discussion on how to mitigate the upcoming negative externalities of substantial cross-domain MEV.

Guillermo Angeris, Alex Evans, Tarun Chitra

Constant function market makers (CFMMs) such as Uniswap, Balancer, Curve, and mStable, among many others, make up some of the largest decentralized exchanges on Ethereum and other blockchains. Because all transactions are public in current implementations, a natural next question is if there exist similar decentralized exchanges which are privacy-preserving; i.e., if a transaction's quantities are hidden from the public view, then an adversary cannot correctly reconstruct the traded quantities from other public information. In this note, we show that privacy is impossible with the usual implementations of CFMMs under most reasonable models of an adversary and provide some mitigating strategies.

Tarun Chitra, Monica Quaintance, Stuart Haber et al.

While many distributed consensus protocols provide robust liveness and consistency guarantees under the presence of malicious actors, quantitative estimates of how economic incentives affect security are few and far between. In this paper, we describe a system for simulating how adversarial agents, both economically rational and Byzantine, interact with a blockchain protocol. This system provides statistical estimates for the economic difficulty of an attack and how the presence of certain actors influences protocol-level statistics, such as the expected time to regain liveness. This simulation system is influenced by the design of algorithmic trading and reinforcement learning systems that use explicit modeling of an agent's reward mechanism to evaluate and optimize a fully autonomous agent. We implement and apply this simulation framework to Kadena's Chainweb, a parallelized Proof-of-Work system, that contains complexity in how miner incentive compliance affects security and censorship resistance. We provide the first formal description of Chainweb that is in the literature and use this formal description to motivate our simulation design. Our simulation results include a phase transition in block height growth rate as a function of shard connectivity and empirical evidence that censorship in Chainweb is too costly for rational miners to engage in. We conclude with an outlook on how simulation can guide and optimize protocol development in a variety of contexts, including Proof-of-Stake parameter optimization and peer-to-peer networking design.