While synthetic data, often generated by LLMs, offers a valuable complement to human-generated data, its misuse can harm performance. Bertrand et al. (2023) and Gerstgrasser et al. (2024) showed self-training on model-generated data leads to degradation. To mitigate this, incorporating a "reliable" verifier to label data has shown promise in preventing such performance collapse (Gillman et al., 2024). A straightforward verification mechanism is to train a reward model on human-annotated data to assess the quality of synthetic data (Lightman et al., 2023; Wang et al., 2024a). However, this approach can be prohibitively expensive and may offer few signals in domains where models exhibit super-human performance. An alternative is to use a stronger model (Chang et al., 2023; Havrilla et al., 2024) for annotation, but this becomes infeasible when the model is at the frontier of current capabilities. A promising solution is to use the model to label its own generations. Motivated by the intuition that "verification is easier than generation", one can hypothesize that the model may act as a better-than-random verifier of its own outputs, enabling self-improvement (Zelikman et al., 2022).

Efficient optimization is critical in pre-training large models (LMs) at scale (McCandlish et al., 2018; Shoeybi et al., 2019; Kaplan et al., 2020). In particular, large-batch training is key to accelerating training, as it enables more efficient parallelism across hardware accelerators (You et al., 2017; Goyal et al., 2018). Specifically, understanding the scaling behavior of the critical batch size (CBS) is essential for optimizing data parallelism, as it defines the point beyond which increasing the batch size may result in computational efficiency degradation. Below the CBS, approximately linear scaling is achievable--doubling the batch size can proportionally reduce the number of optimization steps required to reach a target loss. However, beyond this threshold, further increases in batch size would lead to diminishing returns, making it essential to balance computational efficiency with model performance (McCandlish et al., 2018; Shallue et al., 2019). This trade-off presents a challenge for studying pre-training given resource constraints as practitioners are compelled to navigate difficult decisions in balancing compute, data, and training time. We investigate the scaling laws governing CBS in the context of autoregressive transformerbased language modeling (Vaswani, 2017; Radford et al., 2018). Analyzing CBS in pre-training is challenging due to the absence of a precise formalism relating it to model and data sizes in the literature (McCandlish et al., 2018; Kaplan et al., 2020).

This paper addresses the capacitated periodic review inventory control problem, focusing on a retailer managing multiple products with limited shared resources, such as storage or inbound labor at a facility. Specifically, this paper is motivated by the questions of (1) what does it mean to backtest a capacity control mechanism, (2) can we devise and backtest a capacity control mechanism that is compatible with recent advances in deep reinforcement learning for inventory management? First, because we only have a single historic sample path of Amazon's capacity limits, we propose a method that samples from a distribution of possible constraint paths covering a space of real-world scenarios. This novel approach allows for more robust and realistic testing of inventory management strategies. Second, we extend the exo-IDP (Exogenous Decision Process) formulation of Madeka et al. 2022 to capacitated periodic review inventory control problems and show that certain capacitated control problems are no harder than supervised learning. Third, we introduce a `neural coordinator', designed to produce forecasts of capacity prices, guiding the system to adhere to target constraints in place of a traditional model predictive controller. Finally, we apply a modified DirectBackprop algorithm for learning a deep RL buying policy and a training the neural coordinator. Our methodology is evaluated through large-scale backtests, demonstrating RL buying policies with a neural coordinator outperforms classic baselines both in terms of cumulative discounted reward and capacity adherence (we see improvements of up to 50% in some cases).

We consider regret minimization in repeated games with a very large number of actions. Such games are inherent in the setting of AI safety via debate, and more generally games whose actions are language-based. Existing algorithms for online game playing require computation polynomial in the number of actions, which can be prohibitive for large games. We thus consider oracle-based algorithms, as oracles naturally model access to AI agents. With oracle access, we characterize when internal and external regret can be minimized efficiently. We give a novel efficient algorithm for internal regret minimization whose regret and computation complexity depend logarithmically on the number of actions. This implies efficient oracle-based computation of a correlated equilibrium in large games. We conclude with experiments in the setting of AI Safety via Debate that shows the benefit of insights from our algorithmic analysis.

Accurate uncertainty quantification is crucial for the safe deployment of language models (LMs), and prior research has demonstrated improvements in the calibration of modern LMs. Our study focuses on in-context learning (ICL), a prevalent method for adapting static LMs through tailored prompts, and examines the balance between performance and calibration across a broad spectrum of natural language understanding and reasoning tasks. Through comprehensive experiments, we observe that, with an increasing number of ICL examples, models initially exhibit increased miscalibration before achieving better calibration and miscalibration tends to arise in low-shot settings. Moreover, we find that methods aimed at improving usability, such as fine-tuning and chain-of-thought (CoT) prompting, can lead to miscalibration and unreliable natural language explanations, suggesting that new methods may be required for scenarios where models are expected to be reliable.

In this paper we address the problem of learning and backtesting inventory control policies in the presence of general arrival dynamics -- which we term as a quantity-over-time arrivals model (QOT). We also allow for order quantities to be modified as a post-processing step to meet vendor constraints such as order minimum and batch size constraints -- a common practice in real supply chains. To the best of our knowledge this is the first work to handle either arbitrary arrival dynamics or an arbitrary downstream post-processing of order quantities. Building upon recent work (Madeka et al., 2022) we similarly formulate the periodic review inventory control problem as an exogenous decision process, where most of the state is outside the control of the agent. Madeka et al. (2022) show how to construct a simulator that replays historic data to solve this class of problem. In our case, we incorporate a deep generative model for the arrivals process as part of the history replay. By formulating the problem as an exogenous decision process, we can apply results from Madeka et al. (2022) to obtain a reduction to supervised learning. Finally, we show via simulation studies that this approach yields statistically significant improvements in profitability over production baselines. Using data from an ongoing real-world A/B test, we show that Gen-QOT generalizes well to off-policy data.

Solutions to address the periodic review inventory control problem with nonstationary random demand, lost sales, and stochastic vendor lead times typically involve making strong assumptions on the dynamics for either approximation or simulation, and applying methods such as optimization, dynamic programming, or reinforcement learning. Therefore, it is important to analyze and evaluate any inventory control policy, in particular to see if there is room for improvement. We introduce the concept of an equilibrium policy, a desirable property of a policy that intuitively means that, in hindsight, changing only a small fraction of actions does not result in materially more reward. We provide a light-weight contextual bandit-based algorithm to evaluate and occasionally tweak policies, and show that this method achieves favorable guarantees, both theoretically and in empirical studies.

Imitation Learning (IL) is one of the most widely used methods in machine learning. Yet, while powerful, many works find it is often not able to fully recover the underlying expert behavior [1-3]. However, none of these works deeply investigate the role of scaling up the model and data size. Inspired by recent work in Natural Language Processing (NLP) [4, 5] where "scaling up" has resulted in increasingly more capable LLMs, we investigate whether carefully scaling up model and data size can bring similar improvements in the imitation learning setting. To demonstrate our findings, we focus on the game of NetHack, a challenging environment featuring procedural generation, stochasticity, long-term dependencies, and partial observability. We find IL loss and mean return scale smoothly with the compute budget and are strongly correlated, resulting in power laws for training compute-optimal IL agents with respect to model size and number of samples. We forecast and train several NetHack agents with IL and find they outperform prior state-of-the-art by at least 2x in all settings. Our work both demonstrates the scaling behavior of imitation learning in a challenging domain, as well as the viability of scaling up current approaches for increasingly capable agents in NetHack, a game that remains elusively hard for current AI systems.

A central obstacle in the objective assessment of treatment effect (TE) estimators in randomized control trials (RCTs) is the lack of ground truth (or validation set) to test their performance. In this paper, we provide a novel cross-validation-like methodology to address this challenge. The key insight of our procedure is that the noisy (but unbiased) difference-of-means estimate can be used as a ground truth "label" on a portion of the RCT, to test the performance of an estimator trained on the other portion. We combine this insight with an aggregation scheme, which borrows statistical strength across a large collection of RCTs, to present an end-to-end methodology for judging an estimator's ability to recover the underlying treatment effect. We evaluate our methodology across 709 RCTs implemented in the Amazon supply chain. In the corpus of AB tests at Amazon, we highlight the unique difficulties associated with recovering the treatment effect due to the heavy-tailed nature of the response variables. In this heavy-tailed setting, our methodology suggests that procedures that aggressively downweight or truncate large values, while introducing bias, lower the variance enough to ensure that the treatment effect is more accurately estimated.

In real-world applications of large-scale time series, one often encounters the situation where the temporal patterns of time series, while drifting over time, differ from one another in the same dataset. In this paper, we provably show under such heterogeneity, training a forecasting model with commonly used stochastic optimizers (e.g. SGD) potentially suffers large gradient variance, and thus requires long time training. To alleviate this issue, we propose a sampling strategy named Subgroup Sampling, which mitigates the large variance via sampling over pre-grouped time series. We further introduce SCott, a variance reduced SGD-style optimizer that co-designs subgroup sampling with the control variate method. In theory, we provide the convergence guarantee of SCott on smooth non-convex objectives. Empirically, we evaluate SCott and other baseline optimizers on both synthetic and real-world time series forecasting problems, and show SCott converges faster with respect to both iterations and wall clock time. Additionally, we show two SCott variants that can speed up Adam and Adagrad without compromising generalization of forecasting models.