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We provide a theoretical framework for Reinforcement Learning with Human Feedback (RLHF). We show that when the underlying true reward is linear, under both Bradley-Terry-Luce (BTL) model (pairwise comparison) and Plackett-Luce (PL) model ($K$-wise comparison), MLE converges under certain semi-norm for the family of linear reward. On the other hand, when training a policy based on the learned reward model, we show that MLE fails while a pessimistic MLE provides policies with good performance under certain coverage assumption. We also show that under the PL model, both the true MLE and a different MLE which splits the $K$-wise comparison into pairwise comparisons converge, while the true MLE is asymptotically more efficient. Our results validate the empirical success of the existing RLHF algorithms, and provide new insights for algorithm design. Our analysis can also be applied for the problem of online RLHF and inverse reinforcement learning.

Unsupervised object-centric representation (OCR) learning has recently drawn attention as a new paradigm of visual representation. This is because of its *potential* of being an effective pre-training technique for various downstream tasks in terms of sample efficiency, systematic generalization, and reasoning. Although image-based reinforcement learning (RL) is one of the most important and thus frequently mentioned such downstream tasks, the benefit in RL has surprisingly not been investigated systematically thus far. Instead, most of the evaluations have focused on rather indirect metrics such as segmentation quality and object property prediction accuracy. In this paper, we investigate the effectiveness of OCR pre-training for image-based reinforcement learning via empirical experiments. For systematic evaluation, we introduce a simple object-centric visual RL benchmark and conduct experiments to answer questions such as "Does OCR pre-training improve performance on object-centric tasks?" and "Can OCR pre-training help with out-of-distribution generalization?". Our results provide empirical evidence for valuable insights into the effectiveness of OCR pre-training for RL and the potential limitations of its use in certain scenarios. Additionally, this study also examines the critical aspects of incorporating OCR pre-training in RL, including performance in a visually complex environment and the appropriate pooling layer to aggregate the object representations.

We abstract the features (i.e. learned representations) of multi-modal data into 1) uni-modal features, which can be learned from uni-modal training, and 2) paired features, which can only be learned from cross-modal interactions. Multi-modal models are expected to benefit from cross-modal interactions on the basis of ensuring uni-modal feature learning. However, recent supervised multi-modal late-fusion training approaches still suffer from insufficient learning of uni-modal features on each modality. We prove that this phenomenon does hurt the model's generalization ability. To this end, we propose to choose a targeted late-fusion learning method for the given supervised multi-modal task from Uni-Modal Ensemble (UME) and the proposed Uni-Modal Teacher (UMT), according to the distribution of uni-modal and paired features. We demonstrate that, under a simple guiding strategy, we can achieve comparable results to other complex late-fusion or intermediate-fusion methods on various multi-modal datasets, including VGG-Sound, Kinetics-400, UCF101, and ModelNet40.

We study the variance of stochastic policy gradients (SPGs) with many action samples per state. We derive a many-actions optimality condition, which determines when many-actions SPG yields lower variance as compared to a single-action agent with proportionally extended trajectory. We propose Model-Based Many-Actions (MBMA), an approach leveraging dynamics models for many-actions sampling in the context of SPG. MBMA addresses issues associated with existing implementations of many-actions SPG and yields lower bias and comparable variance to SPG estimated from states in model-simulated rollouts. We find that MBMA bias and variance structure matches that predicted by theory. As a result, MBMA achieves improved sample efficiency and higher returns on a range of continuous action environments as compared to model-free, many-actions, and model-based on-policy SPG baselines.

Spiking neural networks (SNNs) with biologically inspired spatio-temporal dynamics demonstrate superior energy efficiency on neuromorphic architectures. Error backpropagation in SNNs is prohibited by the all-or-none nature of spikes. The existing solution circumvents this problem by a relaxation on the gradient calculation using a continuous function with a constant relaxation de- gree, so-called surrogate gradient learning. Nevertheless, such a solution introduces additional smoothing error on spike firing which leads to the gradients being estimated inaccurately. Thus, how to adaptively adjust the relaxation degree and eliminate smoothing error progressively is crucial. Here, we propose a methodology such that training a prototype neural network will evolve into training an SNN gradually by fusing the learnable relaxation degree into the network with random spike noise. In this way, the network learns adaptively the accurate gradients of loss landscape in SNNs. The theoretical analysis further shows optimization on such a noisy network could be evolved into optimization on the embedded SNN with shared weights progressively. Moreover, The experiments on static images, dynamic event streams, speech, and instrumental sounds show the proposed method achieves state-of-the-art performance across all the datasets with remarkable robustness on different relaxation degrees.

The policy gradient theorem gives a convenient form of the policy gradient in terms of three factors: an action value, a gradient of the action likelihood, and a state distribution involving discounting called the *discounted stationary distribution*. But commonly used on-policy methods based on the policy gradient theorem ignores the discount factor in the state distribution, which is technically incorrect and may even cause degenerate learning behavior in some environments. An existing solution corrects this discrepancy by using $\gamma^t$ as a factor in the gradient estimate. However, this solution is not widely adopted and does not work well in tasks where the later states are similar to earlier states. We introduce a novel distribution correction to account for the discounted stationary distribution that can be plugged into many existing gradient estimators. Our correction circumvents the performance degradation associated with the $\gamma^t$ correction with a lower variance. Importantly, compared to the uncorrected estimators, our algorithm provides improved state emphasis to evade suboptimal policies in certain environments and consistently matches or exceeds the original performance on several OpenAI gym and DeepMind suite benchmarks.

Curriculum learning (CL)- training using samples that are generated and presented in a meaningful order - was introduced in the machine learning context around a decade ago. While CL has been extensively used and analysed empirically, there has been very little mathematical justification for its advantages. We introduce a CL model for learning the class of k-parities on d bits of a binary string with a neural network trained by stochastic gradient descent (SGD). We show that a wise choice of training examples, involving two or more product distributions, allows to reduce significantly the computational cost of learning this class of functions, compared to learning under the uniform distribution. We conduct experiments to support our analysis. Furthermore, we show that for another class of functions - namely the `Hamming mixtures' - CL strategies involving a bounded number of product distributions are not beneficial.

Post-training quantization (PTQ) has been gaining popularity for the deployment of deep neural networks on resource-limited devices since unlike quantization-aware training, neither a full training dataset nor end-to-end training is required at all. As PTQ schemes based on reconstructing each layer or block output turn out to be effective to enhance quantized model performance, recent works have developed algorithms to devise and learn a new weight-rounding scheme so as to better reconstruct each layer or block output. In this work, we propose a simple yet effective new weight-rounding mechanism for PTQ, coined FlexRound, based on element-wise division instead of typical element-wise addition such that FlexRound enables jointly learning a common quantization grid size as well as a different scale for each pre-trained weight. Thanks to the reciprocal rule of derivatives induced by element-wise division, FlexRound is inherently able to exploit pre-trained weights when updating their corresponding scales, and thus, flexibly quantize pre-trained weights depending on their magnitudes. We empirically validate the efficacy of FlexRound on a wide range of models and tasks. To the best of our knowledge, our work is the first to carry out comprehensive experiments on not only image classification and natural language understanding but also natural language generation, assuming a per-tensor uniform PTQ setting. Moreover, we demonstrate, for the first time, that large language models can be efficiently quantized, with only a negligible impact on performance compared to half-precision baselines, achieved by reconstructing the output in a block-by-block manner.

This article introduces a novel structured random matrix composed blockwise from subsampled randomized Hadamard transforms (SRHTs). The block SRHT is expected to outperform well-known dimension reduction maps, including SRHT and Gaussian matrices on distributed architectures. We prove that a block SRHT with enough rows is an oblivious subspace embedding, i.e., an approximate isometry for an arbitrary low-dimensional subspace with high probability. Our estimate of the required number of rows is similar to that of the standard SRHT. This suggests that the two transforms should provide the same accuracy of approximation in the algorithms. The block SRHT can be readily incorporated into randomized methods for computing a low-rank approximation of a large-scale matrix, such as the Nyström method. For completeness, we revisit this method with a discussion of its implementation on distributed architectures.

Incremental learning is a machine learning approach that involves training a model on a sequence of tasks, rather than all tasks at once. This ability to learn incrementally from a stream of tasks is crucial for many real-world applications. However, incremental learning is a challenging problem on graph-structured data, as many graph-related problems involve prediction tasks for each individual node, known as Node-wise Graph Incremental Learning (NGIL). This introduces non-independent and non-identically distributed characteristics in the sample data generation process, making it difficult to maintain the performance of the model as new tasks are added. In this paper, we focus on the inductive NGIL problem, which accounts for the evolution of graph structure (structural shift) induced by emerging tasks. We provide a formal formulation and analysis of the problem, and propose a novel regularization-based technique called Structural-Shift-Risk-Mitigation (SSRM) to mitigate the impact of the structural shift on catastrophic forgetting of the inductive NGIL problem. We show that the structural shift can lead to a shift in the input distribution for the existing tasks, and further lead to an increased risk of catastrophic forgetting. Through comprehensive empirical studies with several benchmark datasets, we demonstrate that our proposed method, Structural-Shift-Risk-Mitigation (SSRM), is flexible and easy to adapt to improve the performance of state-of-the-art GNN incremental learning frameworks in the inductive setting.

This paper proposes Meta-SAGE, a novel approach for improving the scalability of deep reinforcement learning models for combinatorial optimization (CO) tasks. Our method adapts pre-trained models to larger-scale problems in test time by suggesting two components: a scale meta-learner (SML) and scheduled adaptation with guided exploration (SAGE). First, SML transforms the context embedding for subsequent adaptation of SAGE based on scale information. Then, SAGE adjusts the model parameters dedicated to the context embedding for a specific instance. SAGE introduces locality bias, which encourages selecting nearby locations to determine the next location. The locality bias gradually decays as the model is adapted to the target instance. Results show that Meta-SAGE outperforms previous adaptation methods and significantly improves scalability in representative CO tasks. Our source code is available at https://github.com/kaist-silab/meta-sage.

Federated Learning (FL) has been a popular approach to enable collaborative learning on multiple parties without exchanging raw data. However, the model performance of FL may degrade a lot due to non-IID data. While many FL algorithms focus on non-IID labels, FL on non-IID features has largely been overlooked. Different from typical FL approaches, the paper proposes a new learning concept called ADCOL (Adversarial Collaborative Learning) for non-IID features. Instead of adopting the widely used model-averaging scheme, ADCOL conducts training in an adversarial way: the server aims to train a discriminator to distinguish the representations of the parties, while the parties aim to generate a common representation distribution. Our experiments show that ADCOL achieves better performance than state-of-the-art FL algorithms on non-IID features.

Variational autoencoders (VAEs) are one of the deep generative models that have experienced enormous success over the past decades. However, in practice, they suffer from a problem called posterior collapse, which occurs when the posterior distribution coincides, or collapses, with the prior taking no information from the latent structure of the input data into consideration. In this work, we introduce an inverse Lipschitz neural network into the decoder and, based on this architecture, provide a new method that can control in a simple and clear manner the degree of posterior collapse for a wide range of VAE models equipped with a concrete theoretical guarantee. We also illustrate the effectiveness of our method through several numerical experiments.

Long-tailed learning is one of the most challenging problems in visual recognition. There are some studies aiming to solve long-tailed classification from the perspective of feature learning. Recent work proposes to learn the balanced representation by fixing the linear classifier as Equiangular Tight Frame (ETF), since they argue what matters in classification is the structure of the feature, instead of their directions. Holding a different view, in this paper, we show that features with fixed directions may be harmful to the generalization of models, even if it is completely symmetric. To avoid this issue, we propose Representation-Balanced Learning Framework (RBL), which introduces orthogonal matrices to learn directions while maintaining the geometric structure of ETF. Theoretically, our contributions are two-fold: 1). we point out that the feature learning of RBL is insensitive toward training set label distribution, it always learns a balanced representation space. 2). we provide a generalization analysis of proposed RBL through training stability. To analyze the stability of the parameter with orthogonal constraint, we propose a novel training stability analysis paradigm, Two-Parameter Model Stability. Practically, our method is extremely simple in implementation but shows great superiority on several benchmark datasets.

Optimization of atomic structures presents a challenging problem, due to their highly rough and non-convex energy landscape, with wide applications in the fields of drug design, materials discovery, and mechanics. Here, we present a graph reinforcement learning approach, StriderNet, that learns a policy to displace the atoms towards low energy configurations. We evaluate the performance of StriderNet on three complex atomic systems, namely, binary Lennard-Jones particles, calcium silicate hydrates gel, and disordered silicon. We show that StriderNet outperforms all classical optimization algorithms and enables the discovery of a lower energy minimum. In addition, StriderNet exhibits a higher rate of reaching minima with energies, as confirmed by the average over multiple realizations. Finally, we show that StriderNet exhibits inductivity to unseen system sizes that are an order of magnitude different from the training system. All the codes and datasets are available at https://github.com/M3RG-IITD/StriderNET.

Recent works have shown that tackling offline reinforcement learning (RL) with a conditional policy produces promising results. The Decision Transformer (DT) combines the conditional policy approach and a transformer architecture, showing competitive performance against several benchmarks. However, DT lacks stitching ability -- one of the critical abilities for offline RL to learn the optimal policy from sub-optimal trajectories. This issue becomes particularly significant when the offline dataset only contains sub-optimal trajectories. On the other hand, the conventional RL approaches based on Dynamic Programming (such as Q-learning) do not have the same limitation; however, they suffer from unstable learning behaviours, especially when they rely on function approximation in an off-policy learning setting. In this paper, we propose the Q-learning Decision Transformer (QDT) to address the shortcomings of DT by leveraging the benefits of Dynamic Programming (Q-learning). It utilises the Dynamic Programming results to relabel the return-to-go in the training data to then train the DT with the relabelled data. Our approach efficiently exploits the benefits of these two approaches and compensates for each other's shortcomings to achieve better performance.

We study a new connection between a technical measure called $\mu$-conductance that arises in the study of Markov chains for sampling convex bodies and the network community profile that characterizes size-resolved properties of clusters and communities in social and information networks. The idea of $\mu$-conductance is similar to the traditional graph conductance, but disregards sets with small volume. We derive a sequence of optimization problems including a low-rank semi-definite program from which we can derive a lower bound on the optimal $\mu$-conductance value. These ideas give the first theoretically sound bound on the behavior of the network community profile for a wide range of cluster sizes. The algorithm scales up to graphs with hundreds of thousands of nodes and we demonstrate how our framework validates the predicted structures of real-world graphs.

Reasoning is the crux of intellectual thinking. While question answering (QA) tasks are prolific with various computational models and benchmark datasets, they mostly tackle factoid or shallow QA without asking deeper understanding. Dual process theory asserts that human reasoning consists of associative thinking to collect relevant pieces of knowledge and logical reasoning to consciously conclude grounding on evidential rationale. Based on our intensive think-aloud study that revealed the three types of questions: surface, testing, and deep questions, we first propose the QASA benchmark that consists of 1798 novel question answering pairs that require full-stack reasoning on scientific articles in AI and ML fields. Then we propose the QASA approach that tackles the full-stack reasoning with large language models via associative selection, evidential rationale-generation, and systematic composition. Our experimental results show that QASA's full-stack inference outperforms the state-of-the-art InstructGPT by a big margin. We also find that rationale-generation is critical for the performance gain, claiming how we should rethink advanced question answering. The dataset is available at https://github.com/lgresearch/QASA.

The ubiquity of distributed machine learning (ML) in sensitive public domain applications calls for algorithms that protect data privacy, while being robust to faults and adversarial behaviors. Although privacy and robustness have been extensively studied independently in distributed ML, their synthesis remains poorly understood. We present the first tight analysis of the error incurred by any algorithm ensuring robustness against a fraction of adversarial machines, as well as differential privacy (DP) for honest machines' data against any other curious entity. Our analysis exhibits a fundamental trade-off between privacy, robustness, and utility. To prove our lower bound, we consider the case of mean estimation, subject to distributed DP and robustness constraints, and devise reductions to centralized estimation of one-way marginals. We prove our matching upper bound by presenting a new distributed ML algorithm using a high-dimensional robust aggregation rule. The latter amortizes the dependence on the dimension in the error (caused by adversarial workers and DP), while being agnostic to the statistical properties of the data.

Smoothness and low dimensional structures play central roles in improving generalization and stability in learning and statistics. This work combines techniques from semi-infinite constrained learning and manifold regularization to learn representations that are globally smooth on a manifold. To do so, it shows that under typical conditions the problem of learning a Lipschitz continuous function on a manifold is equivalent to a dynamically weighted manifold regularization problem. This observation leads to a practical algorithm based on a weighted Laplacian penalty whose weights are adapted using stochastic gradient techniques. It is shown that under mild conditions, this method estimates the Lipschitz constant of the solution, learning a globally smooth solution as a byproduct. Experiments on real world data illustrate the advantages of the proposed method relative to existing alternatives. Our code is available at https://github.com/JuanCervino/smoothbench.