Adversarial learning has been attracting more and more attention thanks to the fast development of machine learning and artificial intelligence. However, due to the complicated structure of most machine learning models, the mechanism of adversarial attacks is not well interpreted. How to measure the effect of attacks is still not quite clear. In this paper, we investigate the adversarial learning from the perturbation analysis point of view. We characterize the robustness of learning models through the calmness of the solution mapping. In the case of convex clustering models, we identify the conditions under which the clustering results remain the same under perturbations. When the noise level is large, it leads to an attack. Therefore, we propose two bilevel models for adversarial learning where the effect of adversarial learning is measured by some deviation function. Specifically, we systematically study the so-called $δ$-measure and show that under certain conditions, it can be used as a deviation function in adversarial learning for convex clustering models. Finally, we conduct numerical tests to verify the above theoretical results as well as the efficiency of the two proposed bilevel models.

Link functions, which characterize how human preferences are generated from the value function of an RL problem, are a crucial component in designing RLHF algorithms. Almost all RLHF algorithms, including state-of-the-art ones in empirical studies such as DPO and PPO, assume the link function is known to the agent (e.g., a logistic function according to the Bradley-Terry model), which is arguably unrealistic considering the complex nature of human preferences. To avoid link function mis-specification, this paper studies general RLHF problems with unknown link functions. We propose a novel policy optimization algorithm called ZSPO based on a new zeroth-order policy optimization method, where the key is to use human preference to construct a parameter update direction that is positively correlated with the true policy gradient direction. ZSPO achieves it by estimating the sign of the value function difference instead of estimating the gradient from the value function difference, so it does not require knowing the link function. Under mild conditions, ZSPO converges to a stationary policy with a polynomial convergence rate depending on the number of policy iterations and trajectories per iteration. Numerical results also show the superiority of ZSPO under link function mismatch.

Homeostasis is a prevalent process by which living beings maintain their internal milieu around optimal levels. Multiple lines of evidence suggest that living beings learn to act to predicatively ensure homeostasis (allostasis). A classical theory for such regulation is drive reduction, where a function of the difference between the current and the optimal internal state. The recently introduced homeostatic regulated reinforcement learning theory (HRRL), by defining within the framework of reinforcement learning a reward function based on the internal state of the agent, makes the link between the theories of drive reduction and reinforcement learning. The HRRL makes it possible to explain multiple eating disorders. However, the lack of continuous change in the internal state of the agent with the discrete-time modeling has been so far a key shortcoming of the HRRL theory. Here, we propose an extension of the homeostatic reinforcement learning theory to a continuous environment in space and time, while maintaining the validity of the theoretical results and the behaviors explained by the model in discrete time. Inspired by the self-regulating mechanisms abundantly present in biology, we also introduce a model for the dynamics of the agent internal state, requiring the agent to continuously take actions to maintain homeostasis. Based on the Hamilton-Jacobi-Bellman equation and function approximation with neural networks, we derive a numerical scheme allowing the agent to learn directly how its internal mechanism works, and to choose appropriate action policies via reinforcement learning and an appropriate exploration of the environment. Our numerical experiments show that the agent does indeed learn to behave in a way that is beneficial to its survival in the environment, making our framework promising for modeling animal dynamics and decision-making.

In this paper we propose an extension of the notion of deviation-based aggregation function tailored to aggregate multidimensional data. Our objective is both to improve the results obtained by other methods that try to select the best aggregation function for a particular set of data, such as penalty functions, and to reduce the temporal complexity required by such approaches. We discuss how this notion can be defined and present three illustrative examples of the applicability of our new proposal in areas where temporal constraints can be strict, such as image processing, deep learning and decision making, obtaining favourable results in the process.

We present a new generalization error bound, the \emph{PAC-Bayesian transportation bound}, unifying the PAC-Bayesian analysis and the generic chaining method in view of the optimal transportation. The proposed bound is the first PAC-Bayesian framework that characterizes the cost of de-randomization of stochastic predictors facing any Lipschitz loss functions. As an example, we give an upper bound on the de-randomization cost of spectrally normalized neural networks~(NNs) to evaluate how much randomness contributes to the generalization of NNs.

When learning from a batch of logged bandit feedback, the discrepancy between the policy to be learned and the off-policy training data imposes statistical and computational challenges. Unlike classical supervised learning and online learning settings, in batch contextual bandit learning, one only has access to a collection of logged feedback from the actions taken by a historical policy, and expect to learn a policy that takes good actions in possibly unseen contexts. Such a batch learning setting is ubiquitous in online and interactive systems, such as ad platforms and recommendation systems. Existing approaches based on inverse propensity weights, such as Inverse Propensity Scoring (IPS) and Policy Optimizer for Exponential Models (POEM), enjoy unbiasedness but often suffer from large mean squared error. In this work, we introduce a new approach named Maximum Likelihood Inverse Propensity Scoring (MLIPS) for batch learning from logged bandit feedback. Instead of using the given historical policy as the proposal in inverse propensity weights, we estimate a maximum likelihood surrogate policy based on the logged action-context pairs, and then use this surrogate policy as the proposal. We prove that MLIPS is asymptotically unbiased, and moreover, has a smaller nonasymptotic mean squared error than IPS. Such an error reduction phenomenon is somewhat surprising as the estimated surrogate policy is less accurate than the given historical policy. Results on multi-label classification problems and a large- scale ad placement dataset demonstrate the empirical effectiveness of MLIPS. Furthermore, the proposed surrogate policy technique is complementary to existing error reduction techniques, and when combined, is able to consistently boost the performance of several widely used approaches.