We study Nash equilibria learning of a general-sum stochastic game with an unknown transition probability density function. Agents take actions at the current environment state and their joint action influences the transition of the environment state and their immediate rewards. Each agent only observes the environment state and its own immediate reward and is unknown about the actions or immediate rewards of others. We introduce the concepts of weighted asymptotic Nash equilibrium with probability 1 and in probability. For the case with exact pseudo gradients, we design a two-loop algorithm by the equivalence of Nash equilibrium and variational inequality problems. In the outer loop, we sequentially update a constructed strongly monotone variational inequality by updating a proximal parameter while employing a single-call extra-gradient algorithm in the inner loop for solving the constructed variational inequality. We show that if the associated Minty variational inequality has a solution, then the designed algorithm converges to the k^{1/2}-weighted asymptotic Nash equilibrium. Further, for the case with unknown pseudo gradients, we propose a decentralized algorithm, where the G(PO)MDP gradient estimator of the pseudo gradient is provided by Monte-Carlo simulations. The convergence to the k^{1/4} -weighted asymptotic Nash equilibrium in probability is achieved.
Powered by deep representation learning, reinforcement learning (RL) provides an end-to-end learning framework capable of solving self-driving (SD) tasks without manual designs. However, time-varying nonstationary environments cause proficient but specialized RL policies to fail at execution time. For example, an RL-based SD policy trained under sunny days does not generalize well to rainy weather. Even though meta learning enables the RL agent to adapt to new tasks/environments, its offline operation fails to equip the agent with online adaptation ability when facing nonstationary environments. This work proposes an online meta reinforcement learning algorithm based on the \emph{conjectural online lookahead adaptation} (COLA). COLA determines the online adaptation at every step by maximizing the agent's conjecture of the future performance in a lookahead horizon. Experimental results demonstrate that under dynamically changing weather and lighting conditions, the COLA-based self-adaptive driving outperforms the baseline policies in terms of online adaptability. A demo video, source code, and appendixes are available at {\tt https://github.com/Panshark/COLA}
We present MUG, a novel interactive task for multimodal grounding where a user and an agent work collaboratively on an interface screen. Prior works modeled multimodal UI grounding in one round: the user gives a command and the agent responds to the command. Yet, in a realistic scenario, a user command can be ambiguous when the target action is inherently difficult to articulate in natural language. MUG allows multiple rounds of interactions such that upon seeing the agent responses, the user can give further commands for the agent to refine or even correct its actions. Such interaction is critical for improving grounding performances in real-world use cases. To investigate the problem, we create a new dataset that consists of 77,820 sequences of human user-agent interaction on mobile interfaces in which 20% involves multiple rounds of interactions. To establish our benchmark, we experiment with a range of modeling variants and evaluation strategies, including both offline and online evaluation-the online strategy consists of both human evaluation and automatic with simulators. Our experiments show that allowing iterative interaction significantly improves the absolute task completion by 18% over the entire test dataset and 31% over the challenging subset. Our results lay the foundation for further investigation of the problem.
Meta reinforcement learning (meta RL), as a combination of meta-learning ideas and reinforcement learning (RL), enables the agent to adapt to different tasks using a few samples. However, this sampling-based adaptation also makes meta RL vulnerable to adversarial attacks. By manipulating the reward feedback from sampling processes in meta RL, an attacker can mislead the agent into building wrong knowledge from training experience, which deteriorates the agent's performance when dealing with different tasks after adaptation. This paper provides a game-theoretical underpinning for understanding this type of security risk. In particular, we formally define the sampling attack model as a Stackelberg game between the attacker and the agent, which yields a minimax formulation. It leads to two online attack schemes: Intermittent Attack and Persistent Attack, which enable the attacker to learn an optimal sampling attack, defined by an $\epsilon$-first-order stationary point, within $\mathcal{O}(\epsilon^{-2})$ iterations. These attack schemes freeride the learning progress concurrently without extra interactions with the environment. By corroborating the convergence results with numerical experiments, we observe that a minor effort of the attacker can significantly deteriorate the learning performance, and the minimax approach can also help robustify the meta RL algorithms.
Cross-speaker emotion transfer speech synthesis aims to synthesize emotional speech for a target speaker by transferring the emotion from reference speech recorded by another (source) speaker. In this task, extracting speaker-independent emotion embedding from reference speech plays an important role. However, the emotional information conveyed by such emotion embedding tends to be weakened in the process to squeeze out the source speaker's timbre information. In response to this problem, a prosody compensation module (PCM) is proposed in this paper to compensate for the emotional information loss. Specifically, the PCM tries to obtain speaker-independent emotional information from the intermediate feature of a pre-trained ASR model. To this end, a prosody compensation encoder with global context (GC) blocks is introduced to obtain global emotional information from the ASR model's intermediate feature. Experiments demonstrate that the proposed PCM can effectively compensate the emotion embedding for the emotional information loss, and meanwhile maintain the timbre of the target speaker. Comparisons with state-of-the-art models show that our proposed method presents obvious superiority on the cross-speaker emotion transfer task.
We study the decentralized online regularized linear regression algorithm over random time-varying graphs. At each time step, every node runs an online estimation algorithm consisting of an innovation term processing its own new measurement, a consensus term taking a weighted sum of estimations of its own and its neighbors with additive and multiplicative communication noises and a regularization term preventing over-fitting. It is not required that the regression matrices and graphs satisfy special statistical assumptions such as mutual independence, spatio-temporal independence or stationarity. We develop the nonnegative supermartingale inequality of the estimation error, and prove that the estimations of all nodes converge to the unknown true parameter vector almost surely if the algorithm gains, graphs and regression matrices jointly satisfy the sample path spatio-temporal persistence of excitation condition. Especially, this condition holds by choosing appropriate algorithm gains if the graphs are uniformly conditionally jointly connected and conditionally balanced, and the regression models of all nodes are uniformly conditionally spatio-temporally jointly observable, under which the algorithm converges in mean square and almost surely. In addition, we prove that the regret upper bound $\mathcal O(T^{1-\tau}\ln T)$, where $\tau\in (0.5,1)$ is a constant depending on the algorithm gains.
Language models demonstrate both quantitative improvement and new qualitative capabilities with increasing scale. Despite their potentially transformative impact, these new capabilities are as yet poorly characterized. In order to inform future research, prepare for disruptive new model capabilities, and ameliorate socially harmful effects, it is vital that we understand the present and near-future capabilities and limitations of language models. To address this challenge, we introduce the Beyond the Imitation Game benchmark (BIG-bench). BIG-bench currently consists of 204 tasks, contributed by 442 authors across 132 institutions. Task topics are diverse, drawing problems from linguistics, childhood development, math, common-sense reasoning, biology, physics, social bias, software development, and beyond. BIG-bench focuses on tasks that are believed to be beyond the capabilities of current language models. We evaluate the behavior of OpenAI's GPT models, Google-internal dense transformer architectures, and Switch-style sparse transformers on BIG-bench, across model sizes spanning millions to hundreds of billions of parameters. In addition, a team of human expert raters performed all tasks in order to provide a strong baseline. Findings include: model performance and calibration both improve with scale, but are poor in absolute terms (and when compared with rater performance); performance is remarkably similar across model classes, though with benefits from sparsity; tasks that improve gradually and predictably commonly involve a large knowledge or memorization component, whereas tasks that exhibit "breakthrough" behavior at a critical scale often involve multiple steps or components, or brittle metrics; social bias typically increases with scale in settings with ambiguous context, but this can be improved with prompting.
Distribution comparison plays a central role in many machine learning tasks like data classification and generative modeling. In this study, we propose a novel metric, called Hilbert curve projection (HCP) distance, to measure the distance between two probability distributions with high robustness and low complexity. In particular, we first project two high-dimensional probability densities using Hilbert curve to obtain a coupling between them, and then calculate the transport distance between these two densities in the original space, according to the coupling. We show that HCP distance is a proper metric and is well-defined for absolutely continuous probability measures. Furthermore, we demonstrate that the empirical HCP distance converges to its population counterpart at a rate of no more than $O(n^{-1/2d})$ under regularity conditions. To suppress the curse-of-dimensionality, we also develop two variants of the HCP distance using (learnable) subspace projections. Experiments on both synthetic and real-world data show that our HCP distance works as an effective surrogate of the Wasserstein distance with low complexity and overcomes the drawbacks of the sliced Wasserstein distance.