We study a two-sided market, wherein, price-sensitive heterogeneous customers and servers arrive and join their respective queues. A compatible customer-server pair can then be matched by the platform, at which point, they leave the system. Our objective is to design pricing and matching algorithms that maximize the platform's profit, while maintaining reasonable queue lengths. As the demand and supply curves governing the price-dependent arrival rates may not be known in practice, we design a novel online-learning-based pricing policy and establish its near-optimality. In particular, we prove a tradeoff among three performance metrics: OpT1 γq regret, OpTγ{2q average queue length, and OpTγq maximum queue length for γ P p0,1{6s, significantly improving over existing results [1]. Moreover, barring the permissible range of γ, we show that this trade-off between regret and average queue length is optimal up to logarithmic factors under a class of policies, matching the optimal one as in [2] which assumes the demand and supply curves to be known. Our proposed policy has two noteworthy features: a dynamic component that optimizes the tradeoff between low regret and small queue lengths; and a probabilistic component that resolves the tension between obtaining useful samples for fast learning and maintaining small queue lengths.

A certificate that removes outliers sees the data only through its low-degree moments, and an adversary exploits exactly this, hiding corruption where the clean data already looks typical, in the blind spot no bounded-degree test resolves. That blind spot turns out to have an exact size: the Christoffel function of the clean marginal, the very quantity modern data analysis thresholds to detect outliers, here read from the adversary's side as the corruption a bounded-degree certificate cannot remove. We turn this inversion into the organizing principle of the reweighted-hinge approach to robustly learning $γ$-margin halfspaces under malicious noise (Shen, 2025; Zeng and Shen, 2025): the governing resource is the Sum-of-Squares degree of the outlier-removal certificate, and the resolution principle states that the maximal corruption mass which can hide at a center $c$ from a degree-$2t$ certificate is exactly the Christoffel function $λ_{t+1}(c)$ of the clean marginal. Three consequences follow, all against the certificate method (not information-theoretic). A margin-degree tradeoff: certifying the dense pancake to error $ε$ costs SoS degree $Ω(\log(1/ε))$ or margin $Ω(\sqrt{\log(1/ε)}/\sqrt{d})$, explaining why the $\log(1/ε)$ margin Shen (2025) records is forced, with a weighted-Chebyshev reduction making the threshold $2t=Θ((|c|/s)^2)$ tight modulo one classical weighted-extremal estimate. A degree-$2$ outlier barrier: the resolution principle realized as an explicit instance on which degree $2$ is stuck at $η^{1/2}$ while degree $4$ escapes, locating the method's small breakdown rate in the degree, not the analysis. And a degree-$2t$ algorithm tracing the frontier $η^{1-1/2t}$ (recovering Shen (2025) at $t=1$), whose gain is an explicit constant, capped by the pancake density and shown unimprovable by the degree-$2$ barrier.

Recent efforts in neural compression have focused on the rate-distortion-perception (RDP) tradeoff, where the perception constraint ensures the source and reconstruction distributions are close in terms of a statistical divergence. Theoretical work on RDP describes properties of RDP-optimal compressors without providing constructive and low complexity solutions. While classical rate-distortion theory shows that optimal compressors should efficiently pack space, RDP theory additionally shows that infinite randomness shared between the encoder and decoder may be necessary for RDP optimality. In this paper, we propose neural compressors that are low complexity and benefit from high packing efficiency through lattice coding and shared randomness through shared dithering over the lattice cells. For two important settings, namely infinite shared and zero shared randomness, we analyze the RDP tradeoff achieved by our proposed neural compressors and show optimality in both cases. Experimentally, we investigate the roles that these two components of our design, lattice coding and randomness, play in the performance of neural compressors on synthetic and real-world data. We observe that performance improves with more shared randomness and better lattice packing.

Online bipartite matching is a fundamental problem in online optimization, extensively studied both in its integral and fractional forms due to its theoretical significance and practical applications, such as online advertising and resource allocation. Motivated by recent progress in learning-augmented algorithms, we study online bipartite fractional matching when the algorithm is given advice in the form of a suggested matching in each iteration. We develop algorithms for both the vertex-weighted and unweighted variants that provably dominate the naïve "coin flip" strategy of randomly choosing between the advice-following and advice-free algorithms. Moreover, our algorithm for the vertex-weighted setting extends to the AdWords problem under the small bids assumption, yielding a significant improvement over the seminal work of Mahdian, Nazerzadeh, and Saberi (EC 2007, TALG 2012). Complementing our positive results, we establish a hardness bound on the robustness-consistency tradeoff that is attainable by any algorithm.

Reinforcement learning (RL) has become a predominant technique to align language models (LMs) with human preferences or promote outputs which are deemed to be desirable by a given reward function. Standard RL approaches optimize average reward, while methods explicitly focused on reducing the probability of undesired outputs typically come at a cost to average-case performance. To improve this tradeoff, we introduce RePULSe, a new training method that augments the standard RL loss with an additional loss that uses learned proposals to guide sampling low-reward outputs, and then reduces those outputs' probability. We run experiments demonstrating that RePULSe produces a better tradeoff of expected reward versus the probability of undesired outputs and is more adversarially robust, compared to standard RL alignment approaches and alternatives.

Growing evidence suggests that synaptic weights in the brain follow heavy-tailed distributions, yet most theoretical analyses of recurrent neural networks (RNNs) assume Gaussian connectivity. We systematically study the activity of RNNs with random weights drawn from biologically plausible Lévy alpha-stable distributions. While mean-field theory for the infinite system predicts that the quiescent state is always unstable---implying ubiquitous chaos---our finite-size analysis reveals a sharp transition between quiescent and chaotic dynamics. We theoretically predict the gain at which the finite system transitions from quiescent to chaotic dynamics, and validate it through simulations. Compared to Gaussian networks, finite heavy-tailed RNNs exhibit a broader gain regime near the edge of chaos, namely, a slow transition to chaos. However, this robustness comes with a tradeoff: heavier tails reduce the Lyapunov dimension of the attractor, indicating lower effective dimensionality. Our results reveal a biologically aligned tradeoff between the robustness of dynamics near the edge of chaos and the richness of high-dimensional neural activity. By analytically characterizing the transition point in finite-size networks---where mean-field theory breaks down---we provide a tractable framework for understanding dynamics in realistically sized, heavy-tailed neural circuits.

Concept Bottleneck Models (CBMs) have been proposed as a compromise between white-box and black-box models, aiming to achieve interpretability without sacrificing accuracy. The standard training procedure for CBMs is to predefine a candidate set of human-interpretable concepts, extract their values from the training data, and identify a sparse subset as inputs to a transparent prediction model. However, such approaches are often hampered by the tradeoff between exploring a sufficiently large set of concepts versus controlling the cost of obtaining concept extractions, resulting in a large interpretability-accuracy tradeoff. This work investigates a novel approach that sidesteps these challenges: BC-LLM iteratively searches over a potentially infinite set of concepts within a Bayesian framework, in which Large Language Models (LLMs) serve as both a concept extraction mechanism and prior. Even though LLMs can be miscalibrated and hallucinate, we prove that BC-LLM can provide rigorous statistical inference and uncertainty quantification. Across image, text, and tabular datasets, BC-LLM outperforms interpretable baselines and even black-box models in certain settings, converges more rapidly towards relevant concepts, and is more robust to out-of-distribution samples.

Online bidding is a classic optimization problem, with several applications in online decision-making, the design of interruptible systems, and the analysis of approximation algorithms. In this work, we study online bidding under learning-augmented settings that incorporate stochasticity, in either the prediction oracle or the algorithm itself. In the first part, we study bidding under distributional predictions, and find Pareto-optimal algorithms that offer the best-possible tradeoff between the consistency and the robustness of the algorithm. In the second part, we study the power and limitations of randomized bidding algorithms, by presenting upper and lower bounds on the consistency/robustness tradeoffs. Previous works focused predominantly on oracles that do not leverage stochastic information on the quality of the prediction, and deterministic algorithms.

To learn approximately optimal acting policies for decision problems, modern Actor Critic algorithms rely on deep Neural Networks (DNNs) to parameterize the acting policy and greedification operators to iteratively improve it. The reliance on DNNs suggests an improvement that is gradient based, which is per step much less greedy than the improvement possible by greedier operators such as the greedy update used by Q-learning algorithms. On the other hand, slow and steady changes to the policy can also be beneficial for the stability of the learning process, resulting in a tradeoff between greedification and stability. To address this tradeoff, we propose to extend the standard framework of actor critic algorithms with value-improvement: a second greedification operator applied only when updating the policy's value estimate. In this framework the agent can evaluate non-parameterized policies and perform much greedier updates while maintaining the steady gradient-based improvement to the parameterized acting policy. We prove that this approach converges in the popular analysis scheme of generalized Policy Iteration in the finite-horizon domain. Empirically, incorporating value-improvement into the popular off-policy actor-critic algorithms TD3 and SAC significantly improves or matches performance over their respective baselines, across different environments from the DeepMind continuous control domain, with negligible compute and implementation cost.

Large Language Model (LLM) agents are capable of task execution across various domains by autonomously interacting with environments and refining LLM responses based on feedback. However, existing model serving systems are not optimized for the unique demands of serving agents. Compared to classic model serving, agent serving has different characteristics: predictable request pattern, increasing quality requirement, and unique prompt formatting. We identify a key problem for agent serving: LLM serving systems lack session-awareness. They neither perform effective KV cache management nor precisely select the cheapest yet competent model in each round. This leads to a cost-quality tradeoff, and we identify an opportunity to surpass it in an agent serving system. To this end, we introduce AgServe for AGile AGent SERVing.