A.1 Problem Definition We consider two binary classification tasks, with Y The task labels are drawn from two different probabilities. For simplicity, we assume the probability to sample the two label value is balanced, i.e., P (Y = 1) = P (Y = 1) = 0.5. Our conclusion could be extended to unbalanced distribution. In this paper, we mainly study the spurious correlation between task labels. We first consider the setting that we're given infinite samples. If we assume there's no traditional factor-label spurious correlation in single task learning, the bayes optimal classifier will only take each task's causal factor as feature, and assign zero weights to non-causal factors.

We consider regret minimization for Adversarial Markov Decision Processes (AMDPs), where the loss functions are changing over time and adversarially chosen, and the learner only observes the losses for the visited state-action pairs (i.e., bandit feedback). While there has been a surge of studies on this problem using Online-Mirror-Descent (OMD) methods, very little is known about the Follow-the-Perturbed-Leader (FTPL) methods, which are usually computationally more efficient and also easier to implement since it only requires solving an offline planning problem. Motivated by this, we take a closer look at FTPL for learning AMDPs, starting from the standard episodic finite-horizon setting. We find some unique and intriguing difficulties in the analysis and propose a workaround to eventually show that FTPL is also able to achieve near-optimal regret bounds in this case. More importantly, we then find two significant applications: First, the analysis of FTPL turns out to be readily generalizable to delayed bandit feedback with order-optimal regret, while OMD methods exhibit extra difficulties (Jin et al., 2022). Second, using FTPL, we also develop the first no-regret algorithm for learning communicating AMDPs in the infinite-horizon setting with bandit feedback and stochastic transitions. Our algorithm is efficient assuming access to an offline planning oracle, while even for the easier full-information setting, the only existing algorithm (Chandrasekaran and Tewari, 2021) is computationally inefficient.

We study a dynamic pricing problem for third-party platform service fees under strategic, far-sighted customers. In each time period, the platform sets a service fee based on historical data, observes the resulting transaction quantities, and collects revenue. The platform also monitors equilibrium prices influenced by both demand and supply. The objective is to maximize total revenue over a time horizon T. Our problem incorporates three practical challenges: (a) initially, the platform lacks knowledge of the demand side beforehand, necessitating a balance between exploring (learning the demand curve) and exploiting (maximizing revenue) simultaneously; (b) since only equilibrium prices and quantities are observable, traditional Ordinary Least Squares (OLS) estimators would be biased and inconsistent; (c) buyers are rational and strategic, seeking to maximize their consumer surplus and potentially misrepresenting their preferences. To address these challenges, we propose novel algorithmic solutions. Our approach involves: (i) a carefully designed active randomness injection to balance exploration and exploitation effectively; (ii) using non-i.i.d.

We study the overfitting behavior of fully connected deep Neural Networks (NNs) with binary weights fitted to perfectly classify a noisy training set. We consider interpolation using both the smallest NN (having the minimal number of weights) and a random interpolating NN. For both learning rules, we prove overfitting is tempered. Our analysis rests on a new bound on the size of a threshold circuit consistent with a partial function. To the best of our knowledge, ours are the first theoretical results on benign or tempered overfitting that: (1) apply to deep NNs, and (2) do not require a very high or very low input dimension.

Consider the following problem faced by a geographical query service (e.g.

Humans easily interpret expressions that describe unfamiliar situations composed from familiar parts ("greet the pink brontosaurus by the ferris wheel"). Modern neural networks, by contrast, struggle to interpret novel compositions. In this paper, we introduce a new benchmark, gSCAN, for evaluating compositional generalization in situated language understanding. Going beyond a related benchmark that focused on syntactic aspects of generalization, gSCAN defines a language grounded in the states of a grid world, facilitating novel evaluations of acquiring linguistically motivated rules. For example, agents must understand how adjectives such as'small' are interpreted relative to the current world state or how adverbs such as'cautiously' combine with new verbs. We test a strong multi-modal baseline model and a state-of-the-art compositional method finding that, in most cases, they fail dramatically when generalization requires systematic compositional rules.