Ockhamareto: Pareto-Gated Segment-Level Credit Assignment for Concise Unit-Test Generation with Reinforcement Learning

We introduce \textbf{Ockhamareto}, a single-shot GRPO framework for unit-test generation and selection, based on the principles of \emph{Ockham's Razor} and \emph{Pareto Optimality}. Ockhamareto has two principal components: (i)~a \emph{Pareto-gated Bonus} that rewards only rollouts non-dominated in~(mutation, $-$\#tests) space, and (ii)~\emph{Token-level Segment Credit}, which attributes each test's marginal mutation kills back to the tokens of its unit-test block. On the \emph{UnLeakedTestBench~(ULT)}, Ockhamareto \emph{strictly Pareto-dominates} the strongest RL baseline~(\emph{MIST-RL}). Furthermore, it dominates on {\em each and all} optimization objectives, catching more bugs ($49.9\%$ vs $31.3\%$ mutation score at $N{=}5$), using \emph{fewer} tests ($2.60$ vs $4.67$ on average), thereby achieving $3.4\times$ the per-test trade-off improvement. The advantage is found in all four benchmarks~(\emph{HumanEval+}, \emph{MBPP+}, \emph{CodeContests}, \emph{TestGenEval-Lite}): Ockhamareto leads both mutation and coverage metrics on every one, always with the smallest suite. Ockhamareto also outperforms the state-of-the-art at all model scales, adding $+30$--$35$~pp mutation at 4B, 9B, and 27B model sizes. We also show that the knee point of the optimal trade-off between efficiency and effectiveness on the Pareto front is not correlated with obvious more easily computed proxy metrics, such as function size. This finding motivates the Pareto front computation; it is needed to identify this crucial engineering trade-off for each function under test.

Fair Division with Strictly Increasing Valuations: A Tight Threshold for Two-Agent EF1 and PO

We study whether strictly positive marginal values restore the compatibility of envy-freeness up to one good (EF1) and Pareto optimality (PO) for indivisible goods. For two agents, we identify the exact threshold in the number of goods. Every instance with at most seven goods and strictly increasing valuations admits an allocation that is both EF1 and PO, without any submodularity assumption. In contrast, we construct an eight-good instance with normalized, integer-valued, strictly increasing, submodular valuations in which every EF1 allocation is strictly Pareto dominated. Thus, eight goods are necessary and sufficient for a two-agent counterexample. Finally, we strengthen the three-agent NP-hardness result of Chandramouleeswaran and Nimbhorkar (2026): deciding whether an EF1 and PO allocation exists remains NP-hard for normalized, integer-valued, monotone submodular valuations even when zero marginals are confined to eight fixed agent-good pairs, all involving a single agent.

Learning Fair Pareto-Optimal Policies in Multi-Objective Reinforcement Learning

Fairness is an important aspect of decision-making in multi-objective reinforcement learning (MORL), where policies must ensure both optimality and equity across multiple, potentially conflicting objectives. While single-policy MORL methods can learn fair policies for fixed user preferences using welfare functions such as the generalized Gini welfare function (GGF), they fail to provide the diverse set of policies necessary for dynamic or unknown user preferences. To address this limitation, we formalize the fair optimization problem in multi-policy MORL, where the goal is to learn a set of Pareto-optimal policies that ensure fairness across all possible user preferences. Our key technical contributions are threefold: (1) We show that for concave, piecewise-linear welfare functions (e.g., GGF), fair policies remain in the convex coverage set (CCS), which is an approximated Pareto front for linear scalarization. (2) We demonstrate that non-stationary policies, augmented with accrued reward histories, and stochastic policies improve fairness by dynamically adapting to historical inequities. (3) We propose three novel algorithms, which include integrating GGF with multi-policy multi-objective Q-Learning (MOQL), state-augmented multi-policy MOQL for learning non-statoinary policies, and its novel extension for learning stochastic policies. We evaluate our algorithms across various domains and compare our methods against the state-of-the-art MORL baselines. The empirical results show that our methods learn a set of fair policies that accommodate different user preferences.

Multilingual Fine-Tuning via Localized Gradient Conflict Resolution

The rapid evolution of Large Language Models (LLMs) has established cross-lingual versatility as a defining feature of modern systems. However, fine-tuning these models frequently induces negative interference across languages. To address this, we reformulate multilingual fine-tuning as a multi-objective optimization (MOO) problem. Specifically, we introduce Bucket-Level MOO, a scalable distributed framework that applies gradient-based MOO algorithms locally on parameter buckets. This enables conflict-aware updates without the prohibitive communication overhead of reconstructing full gradient vectors. Theoretically, we prove this localized resolution natively enforces Refined Pareto Stationarity, a strictly tighter necessary condition for Pareto optimality. Empirically, Bucket-Level MOO mitigates interference by driving LLMs to construct distinct language-specific dimensions, improving representational separability. Extensive experiments across four base LLMs demonstrate that our method significantly improves both seen and unseen multilingual performance over standard fine-tuning paradigms.