Harnessing the power of human-annotated data through Supervised Fine-Tuning (SFT) is pivotal for advancing Large Language Models (LLMs). In this paper, we delve into the prospect of growing a strong LLM out of a weak one without the need for acquiring additional human-annotated data. We propose a new fine-tuning method called Self-Play fIne-tuNing (SPIN), which starts from a supervised fine-tuned model. At the heart of SPIN lies a self-play mechanism, where the LLM refines its capability by playing against instances of itself. More specifically, the LLM generates its own training data from its previous iterations, refining its policy by discerning these self-generated responses from those obtained from human-annotated data. Our method progressively elevates the LLM from a nascent model to a formidable one, unlocking the full potential of human-annotated demonstration data for SFT. Theoretically, we prove that the global optimum to the training objective function of our method is achieved only when the LLM policy aligns with the target data distribution. Empirically, we evaluate our method on several benchmark datasets including the HuggingFace Open LLM Leaderboard, MT-Bench, and datasets from Big-Bench. Our results show that SPIN can significantly improve the LLM's performance across a variety of benchmarks and even outperform models trained through direct preference optimization (DPO) supplemented with extra GPT-4 preference data. This sheds light on the promise of self-play, enabling the achievement of human-level performance in LLMs without the need for expert opponents.
In this paper, we study the estimation of the $k$-dimensional sparse principal subspace of covariance matrix $\Sigma$ in the high-dimensional setting. We aim to recover the oracle principal subspace solution, i.e., the principal subspace estimator obtained assuming the true support is known a priori. To this end, we propose a family of estimators based on the semidefinite relaxation of sparse PCA with novel regularizations. In particular, under a weak assumption on the magnitude of the population projection matrix, one estimator within this family exactly recovers the true support with high probability, has exact rank-$k$, and attains a $\sqrt{s/n}$ statistical rate of convergence with $s$ being the subspace sparsity level and $n$ the sample size. Compared to existing support recovery results for sparse PCA, our approach does not hinge on the spiked covariance model or the limited correlation condition. As a complement to the first estimator that enjoys the oracle property, we prove that, another estimator within the family achieves a sharper statistical rate of convergence than the standard semidefinite relaxation of sparse PCA, even when the previous assumption on the magnitude of the projection matrix is violated. We validate the theoretical results by numerical experiments on synthetic datasets.
Diffusion models have emerged as powerful tools for high-quality data generation, such as image generation. Despite its success in continuous spaces, discrete diffusion models, which apply to domains such as texts and natural languages, remain under-studied and often suffer from slow generation speed. In this paper, we propose a novel de-randomized diffusion process, which leads to an accelerated algorithm for discrete diffusion models. Our technique significantly reduces the number of function evaluations (i.e., calls to the neural network), making the sampling process much faster. Furthermore, we introduce a continuous-time (i.e., infinite-step) sampling algorithm that can provide even better sample qualities than its discrete-time (finite-step) counterpart. Extensive experiments on natural language generation and machine translation tasks demonstrate the superior performance of our method in terms of both generation speed and sample quality over existing methods for discrete diffusion models.
The exploration-exploitation dilemma has been a central challenge in reinforcement learning (RL) with complex model classes. In this paper, we propose a new algorithm, Monotonic Q-Learning with Upper Confidence Bound (MQL-UCB) for RL with general function approximation. Our key algorithmic design includes (1) a general deterministic policy-switching strategy that achieves low switching cost, (2) a monotonic value function structure with carefully controlled function class complexity, and (3) a variance-weighted regression scheme that exploits historical trajectories with high data efficiency. MQL-UCB achieves minimax optimal regret of $\tilde{O}(d\sqrt{HK})$ when $K$ is sufficiently large and near-optimal policy switching cost of $\tilde{O}(dH)$, with $d$ being the eluder dimension of the function class, $H$ being the planning horizon, and $K$ being the number of episodes. Our work sheds light on designing provably sample-efficient and deployment-efficient Q-learning with nonlinear function approximation.
Accelerated stochastic gradient descent (ASGD) is a workhorse in deep learning and often achieves better generalization performance than SGD. However, existing optimization theory can only explain the faster convergence of ASGD, but cannot explain its better generalization. In this paper, we study the generalization of ASGD for overparameterized linear regression, which is possibly the simplest setting of learning with overparameterization. We establish an instance-dependent excess risk bound for ASGD within each eigen-subspace of the data covariance matrix. Our analysis shows that (i) ASGD outperforms SGD in the subspace of small eigenvalues, exhibiting a faster rate of exponential decay for bias error, while in the subspace of large eigenvalues, its bias error decays slower than SGD; and (ii) the variance error of ASGD is always larger than that of SGD. Our result suggests that ASGD can outperform SGD when the difference between the initialization and the true weight vector is mostly confined to the subspace of small eigenvalues. Additionally, when our analysis is specialized to linear regression in the strongly convex setting, it yields a tighter bound for bias error than the best-known result.
Misunderstandings arise not only in interpersonal communication but also between humans and Large Language Models (LLMs). Such discrepancies can make LLMs interpret seemingly unambiguous questions in unexpected ways, yielding incorrect responses. While it is widely acknowledged that the quality of a prompt, such as a question, significantly impacts the quality of the response provided by LLMs, a systematic method for crafting questions that LLMs can better comprehend is still underdeveloped. In this paper, we present a method named `Rephrase and Respond' (RaR), which allows LLMs to rephrase and expand questions posed by humans and provide responses in a single prompt. This approach serves as a simple yet effective prompting method for improving performance. We also introduce a two-step variant of RaR, where a rephrasing LLM first rephrases the question and then passes the original and rephrased questions together to a different responding LLM. This facilitates the effective utilization of rephrased questions generated by one LLM with another. Our experiments demonstrate that our methods significantly improve the performance of different models across a wide range to tasks. We further provide a comprehensive comparison between RaR and the popular Chain-of-Thought (CoT) methods, both theoretically and empirically. We show that RaR is complementary to CoT and can be combined with CoT to achieve even better performance. Our work not only contributes to enhancing LLM performance efficiently and effectively but also sheds light on a fair evaluation of LLM capabilities. Data and codes are available at https://github.com/uclaml/Rephrase-and-Respond.
The implicit bias towards solutions with favorable properties is believed to be a key reason why neural networks trained by gradient-based optimization can generalize well. While the implicit bias of gradient flow has been widely studied for homogeneous neural networks (including ReLU and leaky ReLU networks), the implicit bias of gradient descent is currently only understood for smooth neural networks. Therefore, implicit bias in non-smooth neural networks trained by gradient descent remains an open question. In this paper, we aim to answer this question by studying the implicit bias of gradient descent for training two-layer fully connected (leaky) ReLU neural networks. We showed that when the training data are nearly-orthogonal, for leaky ReLU activation function, gradient descent will find a network with a stable rank that converges to $1$, whereas for ReLU activation function, gradient descent will find a neural network with a stable rank that is upper bounded by a constant. Additionally, we show that gradient descent will find a neural network such that all the training data points have the same normalized margin asymptotically. Experiments on both synthetic and real data backup our theoretical findings.
We investigate the problem of corruption robustness in offline reinforcement learning (RL) with general function approximation, where an adversary can corrupt each sample in the offline dataset, and the corruption level $\zeta\geq0$ quantifies the cumulative corruption amount over $n$ episodes and $H$ steps. Our goal is to find a policy that is robust to such corruption and minimizes the suboptimality gap with respect to the optimal policy for the uncorrupted Markov decision processes (MDPs). Drawing inspiration from the uncertainty-weighting technique from the robust online RL setting \citep{he2022nearly,ye2022corruptionrobust}, we design a new uncertainty weight iteration procedure to efficiently compute on batched samples and propose a corruption-robust algorithm for offline RL. Notably, under the assumption of single policy coverage and the knowledge of $\zeta$, our proposed algorithm achieves a suboptimality bound that is worsened by an additive factor of $\mathcal O(\zeta \cdot (\text{CC}(\lambda,\hat{\mathcal F},\mathcal Z_n^H))^{1/2} (C(\hat{\mathcal F},\mu))^{-1/2} n^{-1})$ due to the corruption. Here $\text{CC}(\lambda,\hat{\mathcal F},\mathcal Z_n^H)$ is the coverage coefficient that depends on the regularization parameter $\lambda$, the confidence set $\hat{\mathcal F}$, and the dataset $\mathcal Z_n^H$, and $C(\hat{\mathcal F},\mu)$ is a coefficient that depends on $\hat{\mathcal F}$ and the underlying data distribution $\mu$. When specialized to linear MDPs, the corruption-dependent error term reduces to $\mathcal O(\zeta d n^{-1})$ with $d$ being the dimension of the feature map, which matches the existing lower bound for corrupted linear MDPs. This suggests that our analysis is tight in terms of the corruption-dependent term.
We study the federated pure exploration problem of multi-armed bandits and linear bandits, where $M$ agents cooperatively identify the best arm via communicating with the central server. To enhance the robustness against latency and unavailability of agents that are common in practice, we propose the first federated asynchronous multi-armed bandit and linear bandit algorithms for pure exploration with fixed confidence. Our theoretical analysis shows the proposed algorithms achieve near-optimal sample complexities and efficient communication costs in a fully asynchronous environment. Moreover, experimental results based on synthetic and real-world data empirically elucidate the effectiveness and communication cost-efficiency of the proposed algorithms.
Transformers pretrained on diverse tasks exhibit remarkable in-context learning (ICL) capabilities, enabling them to solve unseen tasks solely based on input contexts without adjusting model parameters. In this paper, we study ICL in one of its simplest setups: pretraining a linearly parameterized single-layer linear attention model for linear regression with a Gaussian prior. We establish a statistical task complexity bound for the attention model pretraining, showing that effective pretraining only requires a small number of independent tasks. Furthermore, we prove that the pretrained model closely matches the Bayes optimal algorithm, i.e., optimally tuned ridge regression, by achieving nearly Bayes optimal risk on unseen tasks under a fixed context length. These theoretical findings complement prior experimental research and shed light on the statistical foundations of ICL.