We consider a collaborative learning setting where the goal of each agent is to improve their own model by leveraging the expertise of collaborators, in addition to their own training data. To facilitate the exchange of expertise among agents, we propose a distillation-based method leveraging shared unlabeled auxiliary data, which is pseudo-labeled by the collective. Central to our method is a trust weighting scheme that serves to adaptively weigh the influence of each collaborator on the pseudo-labels until a consensus on how to label the auxiliary data is reached. We demonstrate empirically that our collaboration scheme is able to significantly boost individual models' performance in the target domain from which the auxiliary data is sampled. At the same time, it can provably mitigate the negative impact of bad models on the collective. By design, our method adeptly accommodates heterogeneity in model architectures and substantially reduces communication overhead compared to typical collaborative learning methods.

It's an expensive time to fly. These tips can help lighten the load on your wallet. As a general rule, global instability leads to higher prices, and boy, is the world a doozy right now . Airfare hasn't escaped the tumult: US airfares are up 14.9 percent compared to a year ago, according to NerdWallet, largely due to fuel price spikes linked to disruptions in the Strait of Hormuz caused by blockages, bombs, and blockades. While the medium-term outlook for the airline business isn't great, there are still a few smart and tricky ways to save a little money when flying this summer.

As people increasingly rely on AI chatbots for guidance, even on financial matters, a healthy dose of skepticism is critical. I've used ChatGPT to help me build a budget before, and it was genuinely helpful. After I input my monthly salary as well as my standard utilities and recurring expenses, the chatbot drafted a few solid options, and I tweaked them into penny-pinching perfection. "Millions of people turn to ChatGPT with money-related questions, from understanding debt to building budgets and learning financial concepts," says Niko Felix, an OpenAI spokesperson, when reached for comment. "ChatGPT can be a helpful tool for exploring options, preparing questions, and making financial topics easier to understand, but it is not a substitute for licensed financial professionals." OpenAI's Terms of Use state that the AI tool is not meant to replace professional financial advice.

Importance Sampling (IS) is a method for approximating expectations under a target distribution using independent samples from a proposal distribution and the associated importance weights. In many applications, the target distribution is known only up to a normalization constant, in which case self-normalized IS (SNIS) can be used. While the use of self-normalization can have a positive effect on the dispersion of the estimator, it introduces bias. In this work, we propose a new method, BR-SNIS, whose complexity is essentially the same as that of SNIS and which significantly reduces bias without increasing the variance. This method is a wrapper in the sense that it uses the same proposal samples and importance weights as SNIS, but makes clever use of iterated sampling-importance resampling (i-SIR) to form a bias-reduced version of the estimator. We furnish the proposed algorithm with rigorous theoretical results, including new bias, variance and high-probability bounds, and these are illustrated by numerical examples.

We study finite-sum distributed optimization problems involving a master node and n 1local nodes under the popular δ-similarity and µ-strong convexity conditions. We propose two new algorithms, SVRS and AccSVRS, motivated by previous works. The non-accelerated SVRS method combines the techniques of gradient sliding and variance reduction and achieves a better communication complexity of O(n+ nδ/µ)compared to existing non-accelerated algorithms. Applying the framework proposed in Katyusha X [6], we also develop a directly accelerated version named AccSVRS with the O(n+n3/4 p δ/µ) communication complexity. In contrast to existing results, our complexity bounds are entirely smoothness-free and exhibit superiority in ill-conditioned cases. Furthermore, we establish a nearly matched lower bound to verify the tightness of our AccSVRS method.

While Reinforcement Learning (RL) aims to train an agent from a reward function in a given environment, Inverse Reinforcement Learning (IRL) seeks to recover the reward function from observing an expert's behavior. It is well known that, in general, various reward functions can lead to the same optimal policy, and hence, IRL is ill-defined. However, [1] showed that, if we observe two or more experts with different discount factors or acting in different environments, the reward function can under certain conditions be identified up to a constant. This work starts by showing an equivalent identifiability statement from multiple experts in tabular MDPs based on a rank condition, which is easily verifiable and is shown to be also necessary. We then extend our result to various different scenarios, i.e., we characterize reward identifiability in the case where the reward function can be represented as a linear combination of given features, making it more interpretable, or when we have access to approximate transition matrices. Even when the reward is not identifiable, we provide conditions characterizing when data on multiple experts in a given environment allows to generalize and train an optimal agent in a new environment. Our theoretical results on reward identifiability and generalizability are validated in various numerical experiments.

Bayesian causal discovery aims to infer the posterior distribution over causal models from observed data, quantifying epistemic uncertainty and benefiting downstream tasks. However, computational challenges arise due to joint inference over combinatorial space of Directed Acyclic Graphs (DAGs) and nonlinear functions. Despite recent progress towards efficient posterior inference over DAGs, existing methods are either limited to variational inference on node permutation matrices for linear causal models, leading to compromised inference accuracy, or continuous relaxation of adjacency matrices constrained by a DAG regularizer, which cannot ensure resulting graphs are DAGs. In this work, we introduce a scalable Bayesian causal discovery framework based on a combination of stochastic gradient Markov Chain Monte Carlo (SG-MCMC) and Variational Inference (VI) that overcomes these limitations. Our approach directly samples DAGs from the posterior without requiring any DAG regularization, simultaneously draws function parameter samples and is applicable to both linear and nonlinear causal models. To enable our approach, we derive a novel equivalence to the permutation-based DAG learning, which opens up possibilities of using any relaxed gradient estimator defined over permutations. To our knowledge, this is the first framework applying gradient-based MCMC sampling for causal discovery. Empirical evaluation on synthetic and real-world datasets demonstrate our approach's effectiveness compared to state-of-the-art baselines.