Online Conformal Prediction via Universal Portfolio Algorithms

Online conformal prediction (OCP) seeks prediction intervals that achieve long-run $1-α$ coverage for arbitrary (possibly adversarial) data streams, while remaining as informative as possible. Existing OCP methods often require manual learning-rate tuning to work well, and may also require algorithm-specific analyses. Here, we develop a general regret-to-coverage theory for interval-valued OCP based on the $(1-α)$-pinball loss. Our first contribution is to identify \emph{linearized regret} as a key notion, showing that controlling it implies coverage bounds for any online algorithm. This relies on a black-box reduction that depends only on the Fenchel conjugate of an upper bound on the linearized regret. Building on this theory, we propose UP-OCP, a parameter-free method for OCP, via a reduction to a two-asset portfolio selection problem, leveraging universal portfolio algorithms. We show strong finite-time bounds on the miscoverage of UP-OCP, even for polynomially growing predictions. Extensive experiments support that UP-OCP delivers consistently better size/coverage trade-offs than prior online conformal baselines.

AraMix: Recycling, Refiltering, and Deduplicating to Deliver the Largest Arabic Pretraining Corpus

We present AraMix, a deduplicated Arabic pretraining corpus containing approximately 178 billion tokens across 179 million documents. Rather than scraping the web again, AraMix demonstrates that substantial value lies in systematically reusing and curating existing pretraining datasets: we combine seven publicly available Arabic web datasets, apply quality filtering designed specifically for Arabic text to re-filter some datasets, and perform cross-dataset deduplication, both MinHash and sentence-level. This approach reveals that nearly 60% of tokens across these independently collected corpora are duplicates, redundancy that any new scraping efforts will reproduce. Our work suggests that for lower resource languages, investment in curation pipelines for existing data yields greater returns than additional web crawls, an approach that allowed us to curate the largest heavily filtered publicly available Arabic pretraining corpus.

A Best-of-Both-Worlds Proof for Tsallis-INF without Fenchel Conjugates

In this short note, we present a simple derivation of the best-of-both-world guarantee for the Tsallis-INF multi-armed bandit algorithm from J. Zimmert and Y. Seldin. Tsallis-INF: An optimal algorithm for stochastic and adversarial bandits. Journal of Machine Learning Research, 22(28):1-49, 2021. URL https://jmlr.csail.mit.edu/papers/volume22/19-753/19-753.pdf. In particular, the proof uses modern tools from online convex optimization and avoid the use of conjugate functions. Also, we do not optimize the constants in the bounds in favor of a slimmer proof.

STaR-Bets: Sequential Target-Recalculating Bets for Tighter Confidence Intervals

The construction of confidence intervals for the mean of a bounded random variable is a classical problem in statistics with numerous applications in machine learning and virtually all scientific fields. In particular, obtaining the tightest possible confidence intervals is vital every time the sampling of the random variables is expensive. The current state-of-the-art method to construct confidence intervals is by using betting algorithms. This is a very successful approach for deriving optimal confidence sequences, even matching the rate of law of iterated logarithms. However, in the fixed horizon setting, these approaches are either sub-optimal or based on heuristic solutions with strong empirical performance but without a finite-time guarantee. Hence, no betting-based algorithm guaranteeing the optimal $\mathcal{O}(\sqrt{\frac{\sigma^2\log\frac1\delta}{n}})$ width of the confidence intervals are known. This work bridges this gap. We propose a betting-based algorithm to compute confidence intervals that empirically outperforms the competitors. Our betting strategy uses the optimal strategy in every step (in a certain sense), whereas the standard betting methods choose a constant strategy in advance. Leveraging this fact results in strict improvements even for classical concentration inequalities, such as the ones of Hoeffding or Bernstein. Moreover, we also prove that the width of our confidence intervals is optimal up to an $1+o(1)$ factor diminishing with $n$. The code is available on~https://github.com/vvoracek/STaR-bets-confidence-interval.

Square$χ$PO: Differentially Private and Robust $χ^2$-Preference Optimization in Offline Direct Alignment

In this paper, we theoretically study the offline alignment of language models with human preference feedback, under both preference label corruption and privacy protections. To this end, we propose Square$\chi$PO, a simple one-line change to $\chi$PO where the standard log-loss is replaced by a new square loss over probability. Thanks to the inherent properties of this new loss, we have advanced the state-of-the-art of differentially private and robust offline direct alignment. Specifically, for the local model of label privacy, Square$\chi$PO is the first algorithm that attains an optimal rate based on single-policy concentrability even with general function approximations. It also gives the first result under the central model of privacy protection over both prompts (responses) and labels. On the robustness side against Huber label corruption, Square$\chi$PO is the first alignment method that has a meaningful theoretical guarantee under general function approximations. More importantly, Square$\chi$PO can address privacy protection and corruption simultaneously, where an interesting separation is observed, implying that the order of privacy and corruption matters. Furthermore, we show that Square$\chi$PO can also be easily extended to handle the scenario of the general preference model with state-of-the-art guarantees under corruption and privacy. Last but not least, all of our theoretical guarantees enjoy a unified analysis, building upon a new result on the generalization error bounds of least-square regression under corruption and privacy constraints, which we believe is of independent interest to the community.

New Perspectives on the Polyak Stepsize: Surrogate Functions and Negative Results

The Polyak stepsize has been proven to be a fundamental stepsize in convex optimization, giving near optimal gradient descent rates across a wide range of assumptions. The universality of the Polyak stepsize has also inspired many stochastic variants, with theoretical guarantees and strong empirical performance. Despite the many theoretical results, our understanding of the convergence properties and shortcomings of the Polyak stepsize or its variants is both incomplete and fractured across different analyses. We propose a new, unified, and simple perspective for the Polyak stepsize and its variants as gradient descent on a surrogate loss. We show that each variant is equivalent to minimize a surrogate function with stepsizes that adapt to a guaranteed local curvature. Our general surrogate loss perspective is then used to provide a unified analysis of existing variants across different assumptions. Moreover, we show a number of negative results proving that the non-convergence results in some of the upper bounds is indeed real.

A Unified Theoretical Analysis of Private and Robust Offline Alignment: from RLHF to DPO

In this paper, we theoretically investigate the effects of noisy labels in offline alignment, with a focus on the interplay between privacy and robustness against adversarial corruption. Specifically, under linear modeling assumptions, we present a unified analysis covering both reinforcement learning from human feedback (RLHF) and direct preference optimization (DPO) under different privacy-corruption scenarios, such as Local differential privacy-then-Corruption (LTC), where human preference labels are privatized before being corrupted by an adversary, and Corruption-then-Local differential privacy (CTL), where labels are corrupted before privacy protection. Our analysis leverages a reduction framework that reduces the offline alignment problem under linear modeling assumptions to parameter estimation in logistic regression. This framework allows us to establish an interesting separation result between LTC and CTL, demonstrating that LTC presents a greater challenge than CTL in offline alignment, even under linear models. As important by-products, our findings also advance the state-of-the-art theoretical results in offline alignment under privacy-only or corruption-only scenarios.

Optimal Regret of Bernoulli Bandits under Global Differential Privacy

As sequential learning algorithms are increasingly applied to real life, ensuring data privacy while maintaining their utilities emerges as a timely question. In this context, regret minimisation in stochastic bandits under $\epsilon$-global Differential Privacy (DP) has been widely studied. Unlike bandits without DP, there is a significant gap between the best-known regret lower and upper bound in this setting, though they "match" in order. Thus, we revisit the regret lower and upper bounds of $\epsilon$-global DP algorithms for Bernoulli bandits and improve both. First, we prove a tighter regret lower bound involving a novel information-theoretic quantity characterising the hardness of $\epsilon$-global DP in stochastic bandits. Our lower bound strictly improves on the existing ones across all $\epsilon$ values. Then, we choose two asymptotically optimal bandit algorithms, i.e. DP-KLUCB and DP-IMED, and propose their DP versions using a unified blueprint, i.e., (a) running in arm-dependent phases, and (b) adding Laplace noise to achieve privacy. For Bernoulli bandits, we analyse the regrets of these algorithms and show that their regrets asymptotically match our lower bound up to a constant arbitrary close to 1. This refutes the conjecture that forgetting past rewards is necessary to design optimal bandit algorithms under global DP. At the core of our algorithms lies a new concentration inequality for sums of Bernoulli variables under Laplace mechanism, which is a new DP version of the Chernoff bound. This result is universally useful as the DP literature commonly treats the concentrations of Laplace noise and random variables separately, while we couple them to yield a tighter bound.

New Lower Bounds for Stochastic Non-Convex Optimization through Divergence Composition

We study fundamental limits of first-order stochastic optimization in a range of nonconvex settings, including L-smooth functions satisfying Quasar-Convexity (QC), Quadratic Growth (QG), and Restricted Secant Inequalities (RSI). While the convergence properties of standard algorithms are well-understood in deterministic regimes, significantly fewer results address the stochastic case, where only unbiased and noisy gradients are available. We establish new lower bounds on the number of noisy gradient queries to minimize these classes of functions, also showing that they are tight (up to a logarithmic factor) in all the relevant quantities characterizing each class. Our approach reformulates the optimization task as a function identification problem, leveraging divergence composition arguments to construct a challenging subclass that leads to sharp lower bounds. Furthermore, we present a specialized algorithm in the one-dimensional setting that achieves faster rates, suggesting that certain dimensional thresholds are intrinsic to the complexity of non-convex stochastic optimization.

ATA: Adaptive Task Allocation for Efficient Resource Management in Distributed Machine Learning

Asynchronous methods are fundamental for parallelizing computations in distributed machine learning. They aim to accelerate training by fully utilizing all available resources. However, their greedy approach can lead to inefficiencies using more computation than required, especially when computation times vary across devices. If the computation times were known in advance, training could be fast and resource-efficient by assigning more tasks to faster workers. The challenge lies in achieving this optimal allocation without prior knowledge of the computation time distributions. In this paper, we propose ATA (Adaptive Task Allocation), a method that adapts to heterogeneous and random distributions of worker computation times. Through rigorous theoretical analysis, we show that ATA identifies the optimal task allocation and performs comparably to methods with prior knowledge of computation times. Experimental results further demonstrate that ATA is resource-efficient, significantly reducing costs compared to the greedy approach, which can be arbitrarily expensive depending on the number of workers.