In this paper, we introduce a simple yet effective reward dimension reduction method to tackle the scalability challenges of multi-objective reinforcement learning algorithms. While most existing approaches focus on optimizing two to four objectives, their abilities to scale to environments with more objectives remain uncertain. Our method uses a dimension reduction approach to enhance learning efficiency and policy performance in multi-objective settings. While most traditional dimension reduction methods are designed for static datasets, our approach is tailored for online learning and preserves Pareto-optimality after transformation. We propose a new training and evaluation framework for reward dimension reduction in multi-objective reinforcement learning and demonstrate the superiority of our method in environments including one with sixteen objectives, significantly outperforming existing online dimension reduction methods.

With the rapid advancement of Large Language Models (LLMs), LLM-based autonomous agents have shown the potential to function as digital employees, such as digital analysts, teachers, and programmers. In this paper, we develop an application-level testbed based on the open-source strategy game "Unciv", which has millions of active players, to enable researchers to build a "data flywheel" for studying human-like agents in the "digital players" task. This "Civilization"-like game features expansive decision-making spaces along with rich linguistic interactions such as diplomatic negotiations and acts of deception, posing significant challenges for LLM-based agents in terms of numerical reasoning and long-term planning. Another challenge for "digital players" is to generate human-like responses for social interaction, collaboration, and negotiation with human players. The open-source project can be found at https:/github.com/fuxiAIlab/CivAgent.

Chain-of-thought (CoT) reasoning has enabled large language models (LLMs) to utilize additional computation through intermediate tokens to solve complex tasks. However, we posit that typical reasoning traces contain many redundant tokens, incurring extraneous inference costs. Upon examination of the output distribution of current LLMs, we find evidence on their latent ability to reason more concisely, relative to their default behavior. To elicit this capability, we propose simple fine-tuning methods which leverage self-generated concise reasoning paths obtained by best-of-N sampling and few-shot conditioning, in task-specific settings. Our combined method achieves a 30% reduction in output tokens on average, across five model families on GSM8K and MATH, while maintaining average accuracy. By exploiting the fundamental stochasticity and in-context learning capabilities of LLMs, our self-training approach robustly elicits concise reasoning on a wide range of models, including those with extensive post-training. Code is available at https://github.com/TergelMunkhbat/concise-reasoning

Invariant risk minimization is an important general machine learning framework that has recently been interpreted as a total variation model (IRM-TV). However, how to improve out-of-distribution (OOD) generalization in the IRM-TV setting remains unsolved. In this paper, we extend IRM-TV to a Lagrangian multiplier model named OOD-TV -IRM. We find that the autonomous TV penalty hyperpa-rameter is exactly the Lagrangian multiplier. Thus OOD-TV -IRM is essentially a primal-dual optimization model, where the primal optimization minimizes the entire invariant risk and the dual optimization strengthens the TV penalty. The objective is to reach a semi-Nash equilibrium where the balance between the training loss and OOD generalization is maintained. We also develop a convergent primal-dual algorithm that facilitates an adversarial learning scheme. Experimental results show that OOD-TV -IRM outperforms IRM-TV in most situations. Traditional risk minimization methods such as Empirical Risk Minimization (ERM) are widely used in machine learning. ERM generally assumes that both training and test data come from the same distribution. Based on this assumption, ERM learns model parameters by minimizing the average loss on the training data.

In online advertising, uncertainty calibration aims to adjust a ranking model's probability predictions to better approximate the true likelihood of an event, e.g., a click or a conversion. However, existing calibration approaches may lack the ability to effectively model complex nonlinear relations, consider context features, and achieve balanced performance across different data subsets. To tackle these challenges, we introduce a novel model called Monotonic Calibration Networks, featuring three key designs: a monotonic calibration function (MCF), an order-preserving regularizer, and a field-balance regularizer. The nonlinear MCF is capable of naturally modeling and universally approximating the intricate relations between uncalibrated predictions and the posterior probabilities, thus being much more expressive than existing methods. MCF can also integrate context features using a flexible model architecture, thereby achieving context awareness. The order-preserving and field-balance regularizers promote the monotonic relationship between adjacent bins and the balanced calibration performance on data subsets, respectively. Experimental results on both public and industrial datasets demonstrate the superior performance of our method in generating well-calibrated probability predictions.

Armijo line-search (Armijo-LS) is a standard method to set the step-size for gradient descent (GD). For smooth functions, Armijo-LS alleviates the need to know the global smoothness constant $L$ and adapts to the local smoothness, enabling GD to converge faster. However, existing theoretical analyses of GD with Armijo-LS (GD-LS) do not characterize this fast convergence. We show that if the objective function satisfies a certain non-uniform smoothness condition, GD-LS converges provably faster than GD with a constant $1/L$ step-size (denoted as GD(1/L)). Our results imply that for convex losses corresponding to logistic regression and multi-class classification, GD-LS can converge to the optimum at a linear rate and, hence, improve over the sublinear convergence of GD(1/L). Furthermore, for non-convex losses satisfying gradient domination (for example, those corresponding to the softmax policy gradient in RL or generalized linear models with a logistic link function), GD-LS can match the fast convergence of algorithms tailored for these specific settings. Finally, we prove that under the interpolation assumption, for convex losses, stochastic GD with a stochastic line-search can match the fast convergence of GD-LS.

We study transfer learning for matrix completion in a Missing Not-at-Random (MNAR) setting that is motivated by biological problems. The target matrix $Q$ has entire rows and columns missing, making estimation impossible without side information. To address this, we use a noisy and incomplete source matrix $P$, which relates to $Q$ via a feature shift in latent space. We consider both the active and passive sampling of rows and columns. We establish minimax lower bounds for entrywise estimation error in each setting. Our computationally efficient estimation framework achieves this lower bound for the active setting, which leverages the source data to query the most informative rows and columns of $Q$. This avoids the need for incoherence assumptions required for rate optimality in the passive sampling setting. We demonstrate the effectiveness of our approach through comparisons with existing algorithms on real-world biological datasets.

The inductive bias and generalization properties of large machine learning models are -- to a substantial extent -- a byproduct of the optimization algorithm used for training. Among others, the scale of the random initialization, the learning rate, and early stopping all have crucial impact on the quality of the model learnt by stochastic gradient descent or related algorithms. In order to understand these phenomena, we study the training dynamics of large two-layer neural networks. We use a well-established technique from non-equilibrium statistical physics (dynamical mean field theory) to obtain an asymptotic high-dimensional characterization of this dynamics. This characterization applies to a Gaussian approximation of the hidden neurons non-linearity, and empirically captures well the behavior of actual neural network models. Our analysis uncovers several interesting new phenomena in the training dynamics: $(i)$ The emergence of a slow time scale associated with the growth in Gaussian/Rademacher complexity; $(ii)$ As a consequence, algorithmic inductive bias towards small complexity, but only if the initialization has small enough complexity; $(iii)$ A separation of time scales between feature learning and overfitting; $(iv)$ A non-monotone behavior of the test error and, correspondingly, a `feature unlearning' phase at large times.

Deep learning algorithms have made incredible strides in the past decade yet due to the complexity of these algorithms, the science of deep learning remains in its early stages. Being an experimentally driven field, it is natural to seek a theory of deep learning within the physics paradigm. As deep learning is largely about learning functions and distributions over functions, statistical field theory, a rich and versatile toolbox for tackling complex distributions over functions (fields) is an obvious choice of formalism. Research efforts carried out in the past few years have demonstrated the ability of field theory to provide useful insights on generalization, implicit bias, and feature learning effects. Here we provide a pedagogical review of this emerging line of research.

Large Language Models (LLMs) have demonstrated remarkable performance across diverse domains. However, effectiv ely leveraging their vast knowledge for training smaller downstream model s remains an open challenge, especially in domains like tabular data lea rning, where simpler models are often preferred due to interpretability and efficiency. In this paper, we introduce a novel yet straightforward meth od for incorporating LLM-generated global task feature attributions i nto the training process of smaller networks. Specifically, we propose an attribution-matching regularization term that aligns the training dyna mics of the smaller model with the insights provided by the LLM. By doing so, our approach yields superior performance in few-shot learn ing scenarios. Notably, our method requires only black-box API access to th e LLM, making it easy to integrate into existing training pipeline s with minimal computational overhead. Furthermore, we demonstrate how this method can be used to ad dress common issues in real-world datasets, such as skewness and b ias. By integrating high-level knowledge from LLMs, our approach i mproves generalization, even when training data is limited or imbal anced. We validate its effectiveness through extensive experiments a cross multiple tasks, demonstrating improved learning efficiency and model robustness.