No-Regret Linear Bandits under Gap-Adjusted Misspecification

This work studies linear bandits under a new notion of gap-adjusted misspecification and is an extension of Liu et al. (2023). When the underlying reward function is not linear, existing linear bandits work usually relies on a uniform misspecification parameter $\epsilon$ that measures the sup-norm error of the best linear approximation. This results in an unavoidable linear regret whenever $\epsilon > 0$. We propose a more natural model of misspecification which only requires the approximation error at each input $x$ to be proportional to the suboptimality gap at $x$. It captures the intuition that, for optimization problems, near-optimal regions should matter more and we can tolerate larger approximation errors in suboptimal regions. Quite surprisingly, we show that the classical LinUCB algorithm -- designed for the realizable case -- is automatically robust against such $\rho$-gap-adjusted misspecification with parameter $\rho$ diminishing at $O(1/(d \sqrt{\log T}))$. It achieves a near-optimal $O(\sqrt{T})$ regret for problems that the best-known regret is almost linear in time horizon $T$. We further advance this frontier by presenting a novel phased elimination-based algorithm whose gap-adjusted misspecification parameter $\rho = O(1/\sqrt{d})$ does not scale with $T$. This algorithm attains optimal $O(\sqrt{T})$ regret and is deployment-efficient, requiring only $\log T$ batches of exploration. It also enjoys an adaptive $O(\log T)$ regret when a constant suboptimality gap exists. Technically, our proof relies on a novel self-bounding argument that bounds the part of the regret due to misspecification by the regret itself, and a new inductive lemma that limits the misspecification error within the suboptimality gap for all valid actions in each batch selected by G-optimal design.

Stable Minima Cannot Overfit in Univariate ReLU Networks: Generalization by Large Step Sizes

We study the generalization of two-layer ReLU neural networks in a univariate nonparametric regression problem with noisy labels. This is a problem where kernels (\emph{e.g.} NTK) are provably sub-optimal and benign overfitting does not happen, thus disqualifying existing theory for interpolating (0-loss, global optimal) solutions. We present a new theory of generalization for local minima that gradient descent with a constant learning rate can \emph{stably} converge to. We show that gradient descent with a fixed learning rate $\eta$ can only find local minima that represent smooth functions with a certain weighted \emph{first order total variation} bounded by $1/\eta - 1/2 + \widetilde{O}(\sigma + \sqrt{\mathrm{MSE}})$ where $\sigma$ is the label noise level, $\mathrm{MSE}$ is short for mean squared error against the ground truth, and $\widetilde{O}(\cdot)$ hides a logarithmic factor. Under mild assumptions, we also prove a nearly-optimal MSE bound of $\widetilde{O}(n^{-4/5})$ within the strict interior of the support of the $n$ data points. Our theoretical results are validated by extensive simulation that demonstrates large learning rate training induces sparse linear spline fits. To the best of our knowledge, we are the first to obtain generalization bound via minima stability in the non-interpolation case and the first to show ReLU NNs without regularization can achieve near-optimal rates in nonparametric regression.

OpenBA-V2: Reaching 77.3% High Compression Ratio with Fast Multi-Stage Pruning

Large Language Models (LLMs) have played an important role in many fields due to their powerful capabilities.However, their massive number of parameters leads to high deployment requirements and incurs significant inference costs, which impedes their practical applications. Training smaller models is an effective way to address this problem. Therefore, we introduce OpenBA-V2, a 3.4B model derived from multi-stage compression and continual pre-training from the original 15B OpenBA model. OpenBA-V2 utilizes more data, more flexible training objectives, and techniques such as layer pruning, neural pruning, and vocabulary pruning to achieve a compression rate of 77.3\% with minimal performance loss. OpenBA-V2 demonstrates competitive performance compared to other open-source models of similar size, achieving results close to or on par with the 15B OpenBA model in downstream tasks such as common sense reasoning and Named Entity Recognition (NER). OpenBA-V2 illustrates that LLMs can be compressed into smaller ones with minimal performance loss by employing advanced training objectives and data strategies, which may help deploy LLMs in resource-limited scenarios.

Differentially Private Reinforcement Learning with Self-Play

We study the problem of multi-agent reinforcement learning (multi-agent RL) with differential privacy (DP) constraints. This is well-motivated by various real-world applications involving sensitive data, where it is critical to protect users' private information. We first extend the definitions of Joint DP (JDP) and Local DP (LDP) to two-player zero-sum episodic Markov Games, where both definitions ensure trajectory-wise privacy protection. Then we design a provably efficient algorithm based on optimistic Nash value iteration and privatization of Bernstein-type bonuses. The algorithm is able to satisfy JDP and LDP requirements when instantiated with appropriate privacy mechanisms. Furthermore, for both notions of DP, our regret bound generalizes the best known result under the single-agent RL case, while our regret could also reduce to the best known result for multi-agent RL without privacy constraints. To the best of our knowledge, these are the first line of results towards understanding trajectory-wise privacy protection in multi-agent RL.

Near-Optimal Reinforcement Learning with Self-Play under Adaptivity Constraints

We study the problem of multi-agent reinforcement learning (MARL) with adaptivity constraints -- a new problem motivated by real-world applications where deployments of new policies are costly and the number of policy updates must be minimized. For two-player zero-sum Markov Games, we design a (policy) elimination based algorithm that achieves a regret of $\widetilde{O}(\sqrt{H^3 S^2 ABK})$, while the batch complexity is only $O(H+\log\log K)$. In the above, $S$ denotes the number of states, $A,B$ are the number of actions for the two players respectively, $H$ is the horizon and $K$ is the number of episodes. Furthermore, we prove a batch complexity lower bound $\Omega(\frac{H}{\log_{A}K}+\log\log K)$ for all algorithms with $\widetilde{O}(\sqrt{K})$ regret bound, which matches our upper bound up to logarithmic factors. As a byproduct, our techniques naturally extend to learning bandit games and reward-free MARL within near optimal batch complexity. To the best of our knowledge, these are the first line of results towards understanding MARL with low adaptivity.

OpenBA: An Open-sourced 15B Bilingual Asymmetric seq2seq Model Pre-trained from Scratch

Large language models (LLMs) with billions of parameters have demonstrated outstanding performance on various natural language processing tasks. This report presents OpenBA, an open-sourced 15B bilingual asymmetric seq2seq model, to contribute an LLM variant to the Chinese-oriented open-source model community. We enhance OpenBA with effective and efficient techniques as well as adopt a three-stage training strategy to train the model from scratch. Our solution can also achieve very competitive performance with only 380B tokens, which is better than LLaMA-70B on the BELEBELE benchmark, BLOOM-176B on the MMLU benchmark, GLM-130B on the C-Eval (hard) benchmark. This report provides the main details to pre-train an analogous model, including pre-training data processing, Bilingual Flan data collection, the empirical observations that inspire our model architecture design, training objectives of different stages, and other enhancement techniques. Additionally, we also provide the fine-tuning details of OpenBA on four downstream tasks. We have refactored our code to follow the design principles of the Huggingface Transformers Library, making it more convenient for developers to use, and released checkpoints of different training stages at https://huggingface.co/openBA. More details of our project are available at https://github.com/OpenNLG/openBA.git.

GameEval: Evaluating LLMs on Conversational Games

The rapid advancements in large language models (LLMs) have presented challenges in evaluating those models. Existing evaluation methods are either reference-based or preference based, which inevitably need human intervention or introduce test bias caused by evaluator models. In this paper, we propose GameEval, a novel approach to evaluating LLMs through goal-driven conversational games, overcoming the limitations of previous methods. GameEval treats LLMs as game players and assigns them distinct roles with specific goals achieved by launching conversations of various forms, including discussion, question answering, and voting. We design three unique games with cooperative or adversarial objectives, accompanied by corresponding evaluation metrics, to show how this new paradigm comprehensively evaluates model performance.Through extensive experiments, we show that GameEval can effectively differentiate the capabilities of various LLMs, providing a comprehensive assessment of their integrated abilities to solve complex problems. Our public anonymous code is available at https://github.com/GameEval/GameEval.

Semantically Aligned Task Decomposition in Multi-Agent Reinforcement Learning

The difficulty of appropriately assigning credit is particularly heightened in cooperative MARL with sparse reward, due to the concurrent time and structural scales involved. Automatic subgoal generation (ASG) has recently emerged as a viable MARL approach inspired by utilizing subgoals in intrinsically motivated reinforcement learning. However, end-to-end learning of complex task planning from sparse rewards without prior knowledge, undoubtedly requires massive training samples. Moreover, the diversity-promoting nature of existing ASG methods can lead to the "over-representation" of subgoals, generating numerous spurious subgoals of limited relevance to the actual task reward and thus decreasing the sample efficiency of the algorithm. To address this problem and inspired by the disentangled representation learning, we propose a novel "disentangled" decision-making method, Semantically Aligned task decomposition in MARL (SAMA), that prompts pretrained language models with chain-of-thought that can suggest potential goals, provide suitable goal decomposition and subgoal allocation as well as self-reflection-based replanning. Additionally, SAMA incorporates language-grounded RL to train each agent's subgoal-conditioned policy. SAMA demonstrates considerable advantages in sample efficiency compared to state-of-the-art ASG methods, as evidenced by its performance on two challenging sparse-reward tasks, Overcooked and MiniRTS.

Logarithmic Switching Cost in Reinforcement Learning beyond Linear MDPs

In many real-life reinforcement learning (RL) problems, deploying new policies is costly. In those scenarios, algorithms must solve exploration (which requires adaptivity) while switching the deployed policy sparsely (which limits adaptivity). In this paper, we go beyond the existing state-of-the-art on this problem that focused on linear Markov Decision Processes (MDPs) by considering linear Bellman-complete MDPs with low inherent Bellman error. We propose the ELEANOR-LowSwitching algorithm that achieves the near-optimal regret with a switching cost logarithmic in the number of episodes and linear in the time-horizon $H$ and feature dimension $d$. We also prove a lower bound proportional to $dH$ among all algorithms with sublinear regret. In addition, we show the ``doubling trick'' used in ELEANOR-LowSwitching can be further leveraged for the generalized linear function approximation, under which we design a sample-efficient algorithm with near-optimal switching cost.

Near-Optimal Differentially Private Reinforcement Learning

Motivated by personalized healthcare and other applications involving sensitive data, we study online exploration in reinforcement learning with differential privacy (DP) constraints. Existing work on this problem established that no-regret learning is possible under joint differential privacy (JDP) and local differential privacy (LDP) but did not provide an algorithm with optimal regret. We close this gap for the JDP case by designing an $\epsilon$-JDP algorithm with a regret of $\widetilde{O}(\sqrt{SAH^2T}+S^2AH^3/\epsilon)$ which matches the information-theoretic lower bound of non-private learning for all choices of $\epsilon> S^{1.5}A^{0.5} H^2/\sqrt{T}$. In the above, $S$, $A$ denote the number of states and actions, $H$ denotes the planning horizon, and $T$ is the number of steps. To the best of our knowledge, this is the first private RL algorithm that achieves \emph{privacy for free} asymptotically as $T\rightarrow \infty$. Our techniques -- which could be of independent interest -- include privately releasing Bernstein-type exploration bonuses and an improved method for releasing visitation statistics. The same techniques also imply a slightly improved regret bound for the LDP case.