Incorporating Fairness into Online Price Discrimination In the paper “Fairness-aware online price discrimination with nonparametric demand models,” Xi Chen, Jiameng Lyu, Xuan Zhang, and Yuan Zhou explore how fairness can be integrated into dynamic pricing strategies. The authors propose a model that enforces price fairness constraints, ensuring that price differences between customer groups remain within a specified range. Their approach introduces a novel regret lower bound, which contrasts with the typical regret seen in traditional pricing algorithms. This shift underscores the added complexity of optimizing revenue while maintaining fairness. The study not only advances the understanding of fairness-aware dynamic pricing but also enriches the dynamic pricing literature by offering new lower-bound techniques. These insights may be useful for deriving lower bounds in other problems related to learning optimal prices under constraints. Their work contributes significantly to the growing need for ethical pricing practices in data-driven markets.

Time series data supports many domains (e.g., finance and climate science), but its rapid growth strains storage and computation. Dataset condensation can alleviate this by synthesizing a compact training set that preserves key information. Yet most condensation methods are image-centric and often fail on time series because they miss time-series-specific temporal structure, especially local discriminative motifs such as shapelets. In this work, we propose ShapeCond, a novel and efficient condensation framework for time series classification that leverages shapelet-based dataset knowledge via a shapelet-guided optimization strategy. Our shapelet-assisted synthesis cost is independent of sequence length: longer series yield larger speedups in synthesis (e.g., 29× faster over prior state-of-the-art method CondTSC for time-series condensation, and up to 10,000× over naively using shapelets on the Sleep dataset with 3,000 timesteps). By explicitly preserving critical local patterns, ShapeCond improves downstream accuracy and consistently outperforms all prior state-of-the-art time series dataset condensation methods across extensive experiments. Code is available at https://github.com/lunaaa95/ShapeCond.

In data-driven decision-making in marketing, healthcare, and education, it is desirable to utilize a large amount of data from existing ventures to navigate high-dimensional feature spaces and address data scarcity in new ventures. We explore knowledge transfer in dynamic decision-making by concentrating on batch stationary environments and formally defining task discrepancies through the lens of Markov decision processes (MDPs). We propose a framework of Transferred Fitted Q-Iteration algorithm with general function approximation, enabling the direct estimation of the optimal action-state function Q^* using both target and source data. We establish the relationship between statistical performance and MDP task discrepancy under sieve approximation, shedding light on the impact of source and target sample sizes and task discrepancy on the effectiveness of knowledge transfer. We show that the final learning error of the Q^* function is significantly improved from the single task rate both theoretically and empirically.

Digital firms routinely run many online experiments on shared user populations. When product decisions are compositional, such as combinations of interface elements, flows, messages, or incentives, the number of feasible interventions grows combinatorially, while available traffic remains limited. Overlapping experiments can therefore generate interaction effects that are poorly handled by decentralized A/B testing. We study how to design large-scale factorial experiments when the objective is not to estimate every treatment effect, but to identify a high-performing policy under a fixed experimentation budget. We propose a two-stage design that centralizes overlapping experiments into a single factorial problem and models expected outcomes as a low-rank tensor. In the first stage, the platform samples a subset of intervention combinations, uses tensor completion to infer performance on untested combinations, and eliminates weak factor levels using estimated marginal contributions. In the second stage, it applies sequential halving to the surviving combinations to select a final policy. We establish gap-independent simple-regret bounds and gap-dependent identification guarantees showing that the relevant complexity scales with the degrees of freedom of the low-rank tensor and the separation structure across factor levels, rather than the full factorial size. In an offline evaluation based on a product-bundling problem constructed from 100 million Taobao interactions, the proposed method substantially outperforms one-shot tensor completion and unstructured best-arm benchmarks, especially in low-budget and high-noise settings. These results show how centralized, policy-aware experimentation can make combinatorial product design operationally feasible at platform scale.

Reinforcement learning (RL) has proven effective in strengthening the reasoning capabilities of large language models (LLMs). A widely adopted method, Group Relative Policy Optimization (GRPO), has shown strong empirical results in training DeepSeek-R1. However, GRPO fails to update the policy when all responses within a group are incorrect (i.e., all-negative-sample groups). This limitation underscores a key gap between artificial and human intelligence: unlike humans, who can learn from mistakes, GRPO discards these signals. Our first contribution is to introduce a simple framework that mitigates the all-negative-sample issue by incorporating response diversity within groups using a step-wise judge model, which can be either directly trained or adapted from existing LLMs. We prove that this diversification can accelerate GRPO's learning dynamics in a simplified setting. We also empirically validate the proposed stepwise guided policy optimization (SGPO) method, demonstrating consistent gains across model sizes (7B, 14B, 32B) in offline and online training on 9 benchmarks, including base and distilled variants. Our results highlight two advantages: (i) SGPO surpasses GRPO, especially in the early and mid-training stages where all-negative-sample groups are prevalent; and (ii) SGPO does not require judge models to generate correct answers, differentiating it from knowledge distillation methods.

We consider a high-dimensional dynamic pricing problem under non-stationarity, where a firm sells products to $T$ sequentially arriving consumers that behave according to an unknown demand model with potential changes at unknown times. The demand model is assumed to be a high-dimensional generalized linear model (GLM), allowing for a feature vector in $\mathbb R^d$ that encodes products and consumer information. To achieve optimal revenue (i.e., least regret), the firm needs to learn and exploit the unknown GLMs while monitoring for potential change-points. To tackle such a problem, we first design a novel penalized likelihood-based online change-point detection algorithm for high-dimensional GLMs, which is the first algorithm in the change-point literature that achieves optimal minimax localization error rate for high-dimensional GLMs. A change-point detection assisted dynamic pricing (CPDP) policy is further proposed and achieves a near-optimal regret of order $O(s\sqrt{\Upsilon_T T}\log(Td))$, where $s$ is the sparsity level and $\Upsilon_T$ is the number of change-points. This regret is accompanied with a minimax lower bound, demonstrating the optimality of CPDP (up to logarithmic factors). In particular, the optimality with respect to $\Upsilon_T$ is seen for the first time in the dynamic pricing literature, and is achieved via a novel accelerated exploration mechanism. Extensive simulation experiments and a real data application on online lending illustrate the efficiency of the proposed policy and the importance and practical value of handling non-stationarity in dynamic pricing.

Large language model (LLM) training is often bottlenecked by memory constraints and stochastic gradient noise in extremely high-dimensional parameter spaces. Motivated by empirical evidence that many LLM gradient matrices are effectively low-rank during training, we present an unbiased, memory-efficient, low-rank matrix estimator with the lowest variance that is applicable across common stochastic gradient estimation paradigms. The core idea is to project a high-dimensional stochastic gradient estimator onto a random low-dimensional subspace and lift it back, reducing memory while keeping the estimator unbiased and controlling mean-squared error via an optimally designed projection distribution, including Haar–Stiefel projections. The projection distribution is derived by solving a constrained functional optimization problem, yielding an optimal random projector that guides algorithm design. Empirically, the resulting low-rank gradient estimators deliver both practical memory savings and improved training behavior. In RoBERTa-large fine-tuning, our method attains the lowest peak GPU memory among compared methods (e.g., 3.83GB versus 16.7GB for full BP) while remaining competitive in accuracy; in autoregressive LLM pretraining (LLaMA-20M/60M/100M), our method outperforms the traditional methods, supporting the benefit of the proposed optimal projection strategy.

We study the dynamic joint assortment selection and positioning problem, where the attraction of each product depends on both its intrinsic appeal and its display position under a Multinomial Logit (MNL) choice framework. Our study ranges from the multiplicative position effects model, in which each product's attraction is scaled by a position-specific factor, to a general position effects model assigning independent attraction parameters to every product–position pair to capture heterogeneous synergies. For both models, we design round-based learning algorithms that update decisions after every single feedback, and establish the first regret-optimal characterization. Besides, our round-based algorithms provide the prompt operations needed by modern platforms. For the multiplicative model, we develop a cross-position pairwise maximum likelihood estimator with a clipping mechanism, and prove that our algorithm P2MLE-UCB attains a regret of Õ(√(NT)), matching the lower bound and closing the √(K) gap left by prior epoch-based analyses. For the general model, we establish a minimax lower bound and propose GP2-UCB with a matching upper bound. Moreover, we design an efficient subroutine for the per-round joint assortment and positioning optimization based on Dinkelbach's method and maximum-weight bipartite matching. Numerical experiments on synthetic data and the Expedia dataset show that our algorithms consistently outperform state-of-the-art benchmarks.

Financial agents can turn correct context into an unauthorized effect: a customer-facing commitment, trade, or deployed policy. We present SAGE-Fin, a finance-specific authority-handoff contract that makes the proposed effect, not merely its text, the object of runtime control. SAGE-Fin compiles proposals into typed, adapter-bound candidates; records missing or stale institutional obligations as coverage debt; contracts authority under current market, account, policy, and dialogue state; and requires an exact-artifact receipt whose nominal type matches the consuming response, execution, or policy adapter. Evidence and workflow progress cannot substitute for effect authority, and prior authorization is rechecked after state changes. Across an authored 616-case catalog, five deterministic specifications yield 3,080 outputs; a label-isolated harness obtains 616/616 binary reference-prototype parity, including 3/3 named response-gate fixtures, while 22 tests cover selected paths. These results establish executable conformance, not independent safety accuracy. Separately, SAGE-Fin's response gate processed real customer-facing production requests at a confidential digital-asset platform. An operational team independent of the implementation team reached a strongly positive post-deployment conclusion on practical usefulness and workflow fit, and end-user feedback was also strongly positive. Disclosure permits only the review's independence, stakeholder classes, assessed dimensions, and directional conclusion, so this is qualitative field corroboration rather than an aggregate effect estimate. Three distinct de-identified predecessor failures, with independently confirmed 0/3 interception, ground repeated-emission drift, stale account evidence, and missing escalation state without estimating prevalence or treatment effect.

Agentic Reinforcement Learning (Agentic RL) has shown remarkable potential in large language model-based (LLM) agents. These works can empower LLM agents to tackle complex tasks via multi-step, tool-integrated reasoning. However, an inherent limitation of existing Agentic RL methods is their reliance on a pure on-policy paradigm for exploration, restricting exploration to the agent's self-generated outputs and preventing the discovery of new reasoning perspectives for further improvement. While recent efforts incorporate auxiliary off-policy signals to enhance exploration, they typically utilize full off-policy trajectories for trajectory-level policy estimation, overlooking the necessity for the fine-grained, step-level exploratory dynamics within agentic rollout. In this paper, we revisit exploration in Agentic RL and propose Retrieval-Augmented Policy Optimization (RAPO), a novel RL framework that introduces retrieval to explicitly expand exploration during training. To achieve this, we decompose the Agentic RL training process into two phases: (i) Hybrid-policy Agentic Rollout, and (ii) Retrieval-aware Policy Optimization. Specifically, we propose a Hybrid-policy Agentic Rollout strategy, which allows the agents to continuously reason over the retrieved off-policy step-level traces. It dynamically extends the reasoning receptive field of agents, enabling broader exploration conditioned on external behaviors. Subsequently, we introduce the Retrieval-aware Policy Optimization mechanism, which calibrates the policy gradient estimation with retrieval reward and importance shaping, stabilizing training and prioritizing retrieval-illuminating exploration. Extensive experiments show that RAPO achieves an +5.0

With the fast development of big data, it has been easier than before to learn the optimal decision rule by updating the decision rule recursively and making online decisions. We study the online statistical inference of model parameters in a contextual bandit framework of sequential decision-making. We propose a general framework for online and adaptive data collection environment that can update decision rules via weighted stochastic gradient descent. We allow different weighting schemes of the stochastic gradient and establish the asymptotic normality of the parameter estimator. Our proposed estimator significantly improves the asymptotic efficiency over the previous averaged SGD approach via inverse probability weights. We also conduct an optimality analysis on the weights in a linear regression setting. We provide a Bahadur representation of the proposed estimator and show that the remainder term in the Bahadur representation entails a slower convergence rate compared to classical SGD due to the adaptive data collection.

Modern statistical learning problems often involve multiple related data sets, where learning efficiency on a target set can be improved by utilizing related source sets, while heterogeneity among the source sets may introduce bias. Existing approaches are limited by suboptimal performance in multi-source settings, insufficient use of covariance information, or the computational burden of tuning procedures. We propose a tuning-free and covariance-aware shrinkage framework that constructs shrinkage directions using covariance information to improve efficiency. We establish finite-sample risk bounds that yield an explicit risk-improving interval for the shrinkage size, making the procedure fully data-driven and tuning-free. When multiple source sets are available, we further propose a novel sequential algorithm that shrinks the estimator toward the sources one at a time according to their estimated risk reduction. The proposed algorithm asymptotically attains the oracle risk under mild conditions and is guaranteed to improve over the single-step shrinkage method in the literature. The framework is further extended to general smooth M-estimation problems via a local quadratic approximation. Numerical studies show substantial gains over competing methods, especially when the source data sets are highly heterogeneous.

We study transfer learning for contextual joint assortment-pricing under a multinomial logit choice model with bandit feedback. A seller operates across multiple related markets and observes only posted prices and realized purchases. While data from source markets can accelerate learning in a target market, cross-market differences in customer preferences may introduce systematic bias if pooled indiscriminately. We model heterogeneity through a structured utility shift, where markets share a common contextual utility structure but differ along a sparse set of latent preference coordinates. Building on this, we develop Transfer Joint Assortment-Pricing (TJAP), a bias-aware framework that combines aggregate-then-debias estimation with a UCB-style policy. TJAP constructs two-radius confidence bounds that separately capture statistical uncertainty and transfer-induced bias, uniformly over continuous prices. We establish matching minimax regret bounds of order Õ(d√(T/1+H) + s_0√(T)),revealing a transparent variance-bias tradeoff: transfer accelerates learning along shared preference directions, while heterogeneous components impose an irreducible adaptation cost. Numerical experiments corroborate the theory, showing that TJAP outperforms both target-only learning and naive pooling while remaining robust to cross-market differences.

Long-context and memory systems usually treat personalization as a recall problem. In practice, many failures occur later, when a system commits: it turns noisy hints into hard constraints, drops rare witnesses, forgets downstream obligations, or answers despite infeasibility. We introduce Contract-Bounded Evidence Activation (CBEA) with Lexicographic Commitment Validation (LCV). CBEA activates a bounded evidence set using typed coverage, tail witnesses, and consequence debt; LCV validates structured commitments before prose and routes infeasible states to repair, abstention, or recontract. Across 360 fixtures and three generation backends, CBEA+LCV reaches zero failures within validator scope at 0.49-0.60 availability over attempted runs. Raw and long-context baselines with the same LCV gate reach zero only at 0.003-0.092. A shadow oracle diagnostic marks the limit: CBEA+LCV recalls 0.012 of uncompiled visible facts, while raw recalls 0.53. The result is a bounded operating point: explicit commitment control and 74-75

We study online bipartite matching with reusable server capacity and non-stationary rewards. Jobs arrive sequentially, reveal compatible servers, reward rates, and processing durations, and must be accepted or rejected irrevocably. An accepted job occupies one unit of server capacity only during its processing interval, so an assignment may displace an unknown sequence of future jobs. Existing guarantees are typically calibrated by a global reward range, which can become arbitrarily large when rewards drift over a long horizon. We instead impose a locally bounded reward condition: reward rates of jobs that can compete for the same server within a relevant time window differ by at most a factor δ. Under this condition, we develop two BALANCE-type algorithms with time-aware opportunity-cost losses. TS-BAL maximizes cumulative blocking losses over feasible reuse schedules and achieves a competitive ratio of 2ln(δD)+𝒪(lnln(δ∨ D)). GR-BAL uses a greedy relaxation of this loss and achieves ln(δD)+𝒪(lnln(δ∨ D)), matching a lower bound of ln(δD) in the leading term. Numerical experiments demonstrate robust performance under substantial global reward drift and favorable finite-capacity performance.

In this article, we consider a multi-stage assortment optimization problem with multinomial logit (MNL) choice modeling under resource knapsack constraints. Given the current resource inventory levels, the retailer makes an assortment decision at each period, and the goal of the retailer is to maximize the total profit from purchases. With the exact optimal dynamic assortment solution being computationally intractable, a practical strategy is to adopt the re-solving technique that periodically re-optimizes deterministic linear programs (LPs) arising from fluid approximation. However, the fractional structure of MNL makes the fluid approximation in assortment optimization non-linear, which brings new technical challenges. To address this challenge, we propose a new epoch-based re-solving algorithm that effectively transforms the denominator of the objective into the constraint, so that the re-solving technique is applied to a linear program with additional slack variables amenable to practical computations and theoretical analysis. Theoretically, we prove that the regret (i.e., the gap between the re-solving policy and the optimal objective of the fluid approximation) scales logarithmically with the length of time horizon and resource capacities.

We study how an e-commerce firm should make real-time fulfillment decisions in a two-layer distribution network when multi-item customer orders arrive sequentially and future demand is unknown. The central managerial tension is whether to use scarce front distribution center (FDC) inventory to save current fulfillment cost or preserve that inventory for future orders that may be more valuable to serve locally. We formulate an adversarial online model with multiple FDCs, one regional distribution center (RDC), multi-unit multi-item orders, and item-specific and time-varying variable costs. Our theoretical objective is to characterize when simple, interpretable, and implementable fulfillment rules can perform nearly as well as an optimal clairvoyant planner. We develop a family of Gated Priority-based Greedy policies, derive competitive-ratio guarantees under both time-varying and time-invariant cost structures, and establish matching or near-matching lower bounds for any online algorithm. Numerical experiments show that the proposed policies perform strongly relative to generalized myopic and forecast-based benchmarks. The analysis yields managerial guidance on when local inventory should be protected, when splitting orders is worth the fixed-cost burden, and how the relative magnitudes of fixed and variable costs determine the value of more sophisticated optimization.

Direct alignment methods are increasingly used to align large language models (LLMs) with human preferences. However, many real-world alignment problems involve multiple conflicting objectives, where naive aggregation of preferences can lead to unstable training and poor trade-offs. In particular, weighted loss methods may fail to identify update directions that simultaneously improve all objectives, and existing multi-objective approaches often rely on explicit reward models, introducing additional complexity and distorting user-specified preferences. The contributions of this paper are two-fold. First, we propose a eward-free lignment framework for onflicted bjectives (RACO) that directly leverages pairwise preference data and resolves gradient conflicts via a novel clipped variant of conflict-averse gradient descent. We provide convergence guarantees to Pareto-critical points that respect user-specified objective weights, and further show that clipping can strictly improve convergence rate in the two-objective setting. Second, we improve our method using some heuristics and conduct experiments to demonstrate the compatibility of the proposed framework for LLM alignment. Both qualitative and quantitative evaluations on multi-objective summarization and safety alignment tasks across multiple LLM families (Qwen 3, Llama 3, Gemma 3) show that our method consistently achieves better Pareto trade-offs compared to existing multi-objective alignment baselines.

This paper examines the exploration–exploitation trade-off in reinforcement learning with verifiable rewards (RLVR), a framework for improving the reasoning of Large Language Models (LLMs). Recent studies suggest that RLVR can elicit strong mathematical reasoning in LLMs through two seemingly paradoxical mechanisms: \textit{spurious rewards}, which suppress exploitation by rewarding outcomes unrelated to the ground truth, and \textit{entropy minimization}, which suppresses exploration by pushing the model toward more confident and deterministic outputs, highlighting a puzzling dynamic: both discouraging exploitation and discouraging exploration improve reasoning performance, yet the underlying principles that reconcile these effects remain poorly understood. We focus on two fundamental questions: (i) how policy entropy relates to performance, and (ii) whether spurious rewards yield gains, potentially through the interplay of clipping bias and model contamination. Our results show that clipping bias under spurious rewards reduces policy entropy, leading to more confident and deterministic outputs, while entropy minimization alone is insufficient for improvement. We further propose a reward-misalignment model explaining why spurious rewards can enhance performance beyond contaminated settings. Our findings clarify the mechanisms behind spurious-reward benefits and provide principles for more effective RLVR training.

Deeper modern architectures are costly to train, making hyperparameter transfer preferable to expensive repeated tuning. Maximal Update Parametrization (μP) helps explain why many hyperparameters transfer across width. Yet depth scaling is less understood for modern architectures, whose computation graphs contain multiple parallel paths and residual aggregation. To unify various non-recurrent multi-path neural networks such as CNNs, ResNets, and Transformers, we introduce a graph-based notion of effective depth. Under stabilizing initializations and a maximal-update criterion, we show that the optimal learning rate decays with effective depth following a universal -3/2 power law. Here, the maximal-update criterion maximizes the typical one-step representation change at initialization without causing instability, and effective depth is the minimal path length from input to output, counting layers and residual additions. Experiments across diverse architectures confirm the predicted slope and enable reliable zero-shot transfer of learning rates across depths and widths, turning depth scaling into a predictable hyperparameter-transfer problem.