Reinforcement learning (RL) has achieved phenomenal success in various domains. However, its data-driven nature also introduces new vulnerabilities that can be exploited by malicious opponents. Recent work shows that a well-trained RL agent can be easily manipulated by strategically perturbing its state observations at the test stage. Existing solutions either introduce a regularization term to improve the smoothness of the trained policy against perturbations or alternatively train the agent's policy and the attacker's policy. However, the former does not provide sufficient protection against strong attacks, while the latter is computationally prohibitive for large environments. In this work, we propose a new robust RL algorithm for deriving a pessimistic policy to safeguard against an agent's uncertainty about true states. This approach is further enhanced with belief state inference and diffusion-based state purification to reduce uncertainty. Empirical results show that our approach obtains superb performance under strong attacks and has a comparable training overhead with regularization-based methods. As one of the major paradigms for data-driven control, reinforcement learning (RL) provides a principled and solid framework for sequential decision-making under uncertainty. By incorporating the approximation capacity of deep neural networks, deep reinforcement learning (DRL) has found impressive applications in robotics (Levine et al., 2016), large generative models (OpenAI, 2023), and autonomous driving (Kiran et al., 2021), and obtained super-human performance in tasks such as Go (Silver et al., 2016) and Gran Turismo (Wurman et al., 2022). However, an RL agent is subject to various types of attacks, including state and reward perturbation, action space manipulation, and model inference and poisoning (Ilahi et al., 2022). Recent studies have shown that an RL agent can be manipulated by poisoning its observation (Huang et al., 2017; Zhang et al., 2020a) and reward signals (Huang & Zhu, 2019), and a well-trained RL agent can be easily defeated by a malicious opponent behaving unexpectedly (Gleave et al., 2020). In particular, recent research has demonstrated the brittleness (Zhang et al., 2020a; Sun et al., 2021) of existing RL algorithms in the face of adversarial state perturbations, where a malicious agent strategically and stealthily perturbs the observations of a trained RL agent, causing a significant loss of cumulative reward. Such an attack can be implemented in practice by exploiting the defects in the agent's perception component, e.g., sensors and communication channels. This raises significant concerns when applying RL techniques in security and safety-critical domains.

In environments like offices, the duration of a robot's navigation between two locations may vary over time. For instance, reaching a kitchen may take more time during lunchtime since the corridors are crowded with people heading the same way. In this work, we address the problem of routing in such environments with tasks expressed in Metric Interval Temporal Logic (MITL) - a rich robot task specification language that allows us to capture explicit time requirements. Our objective is to find a strategy that maximizes the temporal robustness of the robot's MITL task. As the first step towards a solution, we define a Mixed-integer linear programming approach to solving the task planning problem over a Varying Weighted Transition System, where navigation durations are deterministic but vary depending on the time of day. Then, we apply this planner to optimize for MITL temporal robustness in Markov Decision Processes, where the navigation durations between physical locations are uncertain, but the time-dependent distribution over possible delays is known. Finally, we develop a receding horizon planner for Markov Decision Processes that preserves guarantees over MITL temporal robustness. We show the scalability of our planning algorithms in simulations of robotic tasks.

This paper presents a method of unsupervised learning of harmonic analysis based on a hidden semi-Markov model (HSMM). We introduce the chord quality templates, which specify the probability of pitch class emissions given a root note and a chord quality. Other probability distributions that comprise the HSMM are automatically learned via unsupervised learning, which has been a challenge in existing research. The results of the harmonic analysis of the proposed model were evaluated using existing labeled data. While our proposed method has yet to perform as well as existing models that used supervised learning and complex rule design, it has the advantage of not requiring expensive labeled data or rule elaboration. Furthermore, we also show how to recognize the tonic without prior knowledge, based on the transition probabilities of the Markov model.

Given time series data, how can we answer questions like "what will happen in the future?" and "how did we get here?" These sorts of probabilistic inference questions are challenging when observations are high-dimensional. In this paper, we show how these questions can have compact, closed form solutions in terms of learned representations. The key idea is to apply a variant of contrastive learning to time series data. Prior work already shows that the representations learned by contrastive learning encode a probability ratio. By extending prior work to show that the marginal distribution over representations is Gaussian, we can then prove that joint distribution of representations is also Gaussian. Taken together, these results show that representations learned via temporal contrastive learning follow a Gauss-Markov chain, a graphical model where inference (e.g., prediction, planning) over representations corresponds to inverting a low-dimensional matrix. In one special case, inferring intermediate representations will be equivalent to interpolating between the learned representations. We validate our theory using numerical simulations on tasks up to 46-dimensions.

Recent works have argued that high-level semantic concepts are encoded "linearly" in the representation space of large language models. In this work, we study the origins of such linear representations. To that end, we introduce a simple latent variable model to abstract and formalize the concept dynamics of the next token prediction. We use this formalism to show that the next token prediction objective (softmax with cross-entropy) and the implicit bias of gradient descent together promote the linear representation of concepts. Experiments show that linear representations emerge when learning from data matching the latent variable model, confirming that this simple structure already suffices to yield linear representations. We additionally confirm some predictions of the theory using the LLaMA-2 large language model, giving evidence that the simplified model yields generalizable insights.

Traditional approaches in mental health research apply General Linear Models (GLM) to describe the longitudinal dynamics of observed psycho-behavioral measurements (questionnaire summary scores). Similarly, GLMs are also applied to characterize relationships between neurobiological measurements (regional fMRI signals) and perceptual stimuli or other regional signals. While these methods are useful for exploring linear correlations among the isolated signals of those constructs (i.e., summary scores or fMRI signals), these classical frameworks fall short in providing insights into the comprehensive system-level dynamics underlying observable changes. Hidden Markov Models (HMM) are a statistical model that enable us to describe the sequential relations among multiple observable constructs, and when applied through the lens of Finite State Automata (FSA), can provide a more integrated and intuitive framework for modeling and understanding the underlying controller (the prescription for how to respond to inputs) that fundamentally defines any system, as opposed to linearly correlating output signals produced by the controller. We present a simple and intuitive HMM processing pipeline vcHMM (See Preliminary Data) that highlights FSA theory and is applicable for both behavioral analysis of questionnaire data and fMRI data. HMMs offer theoretic promise as they are computationally equivalent to the FSA, the control processor of a Turing Machine (TM) The dynamic programming Viterbi algorithm is used to leverage the HMM model. It efficiently identifies the most likely sequence of hidden states. The vcHMM pipeline leverages this grammar to understand how behavior and neural activity relate to depression.

This paper proposes a scalable distributed policy gradient method and proves its convergence to near-optimal solution in multi-agent linear quadratic networked systems. The agents engage within a specified network under local communication constraints, implying that each agent can only exchange information with a limited number of neighboring agents. On the underlying graph of the network, each agent implements its control input depending on its nearby neighbors' states in the linear quadratic control setting. We show that it is possible to approximate the exact gradient only using local information. Compared with the centralized optimal controller, the performance gap decreases to zero exponentially as the communication and control ranges increase. We also demonstrate how increasing the communication range enhances system stability in the gradient descent process, thereby elucidating a critical trade-off. The simulation results verify our theoretical findings.

Reward hacking occurs when an agent performs very well with respect to a "proxy" reward function (which may be hand-specified or learned), but poorly with respect to the unknown true reward. Since ensuring good alignment between the proxy and true reward is extremely difficult, one approach to prevent reward hacking is optimizing the proxy conservatively. Prior work has particularly focused on enforcing the learned policy to behave similarly to a "safe" policy by penalizing the KL divergence between their action distributions (AD). However, AD regularization doesn't always work well since a small change in action distribution at a single state can lead to potentially calamitous outcomes, while large changes might not be indicative of any dangerous activity. Our insight is that when reward hacking, the agent visits drastically different states from those reached by the safe policy, causing large deviations in state occupancy measure (OM). Thus, we propose regularizing based on the OM divergence between policies instead of AD divergence to prevent reward hacking. We theoretically establish that OM regularization can more effectively avoid large drops in true reward. Then, we empirically demonstrate in a variety of realistic environments that OM divergence is superior to AD divergence for preventing reward hacking by regularizing towards a safe policy. Furthermore, we show that occupancy measure divergence can also regularize learned policies away from reward hacking behavior. Our code and data are available at https://github.com/cassidylaidlaw/orpo

The generalized linear mixed model (GLMM) is a popular statistical approach for handling correlated data, and is used extensively in applications areas where big data is common, including biomedical data settings. The focus of this paper is scalable statistical inference for the GLMM, where we define statistical inference as: (i) estimation of population parameters, and (ii) evaluation of scientific hypotheses in the presence of uncertainty. Artificial intelligence (AI) learning algorithms excel at scalable statistical estimation, but rarely include uncertainty quantification. In contrast, Bayesian inference provides full statistical inference, since uncertainty quantification results automatically from the posterior distribution. Unfortunately, Bayesian inference algorithms, including Markov Chain Monte Carlo (MCMC), become computationally intractable in big data settings. In this paper, we introduce a statistical inference algorithm at the intersection of AI and Bayesian inference, that leverages the scalability of modern AI algorithms with guaranteed uncertainty quantification that accompanies Bayesian inference. Our algorithm is an extension of stochastic gradient MCMC with novel contributions that address the treatment of correlated data (i.e., intractable marginal likelihood) and proper posterior variance estimation. Through theoretical and empirical results we establish our algorithm's statistical inference properties, and apply the method in a large electronic health records database.

Human trajectory data produced by daily mobile devices has proven its usefulness in various substantial fields such as urban planning and epidemic prevention. In terms of the individual privacy concern, human trajectory simulation has attracted increasing attention from researchers, targeting at offering numerous realistic mobility data for downstream tasks. Nevertheless, the prevalent issue of data scarcity undoubtedly degrades the reliability of existing deep learning models. In this paper, we are motivated to explore the intriguing problem of mobility transfer across cities, grasping the universal patterns of human trajectories to augment the powerful Transformer with external mobility data. There are two crucial challenges arising in the knowledge transfer across cities: 1) how to transfer the Transformer to adapt for domain heterogeneity; 2) how to calibrate the Transformer to adapt for subtly different long-tail frequency distributions of locations. To address these challenges, we have tailored a Cross-city mObiLity trAnsformer (COLA) with a dedicated model-agnostic transfer framework by effectively transferring cross-city knowledge for human trajectory simulation. Firstly, COLA divides the Transformer into the private modules for city-specific characteristics and the shared modules for city-universal mobility patterns. Secondly, COLA leverages a lightweight yet effective post-hoc adjustment strategy for trajectory simulation, without disturbing the complex bi-level optimization of model-agnostic knowledge transfer. Extensive experiments of COLA compared to state-of-the-art single-city baselines and our implemented cross-city baselines have demonstrated its superiority and effectiveness. The code is available at https://github.com/Star607/Cross-city-Mobility-Transformer.