Parameswaran Kamalaruban

Umang Bhatt, Valerie Chen, Katherine M. Collins et al. · cambridge, cmu

Individual human decision-makers may benefit from different forms of support to improve decision outcomes, but when each form of support will yield better outcomes? In this work, we posit that personalizing access to decision support tools can be an effective mechanism for instantiating the appropriate use of AI assistance. Specifically, we propose the general problem of learning a decision support policy that, for a given input, chooses which form of support to provide to decision-makers for whom we initially have no prior information. We develop $\texttt{Modiste}$, an interactive tool to learn personalized decision support policies. $\texttt{Modiste}$ leverages stochastic contextual bandit techniques to personalize a decision support policy for each decision-maker and supports extensions to the multi-objective setting to account for auxiliary objectives like the cost of support. We find that personalized policies outperform offline policies, and, in the cost-aware setting, reduce the incurred cost with minimal degradation to performance. Our experiments include various realistic forms of support (e.g., expert consensus and predictions from a large language model) on vision and language tasks. Our human subject experiments validate our computational experiments, demonstrating that personalization can yield benefits in practice for real users, who interact with $\texttt{Modiste}$.

Georgios Tzannetos, Bárbara Gomes Ribeiro, Parameswaran Kamalaruban et al.

We consider the problem of curriculum design for reinforcement learning (RL) agents in contextual multi-task settings. Existing techniques on automatic curriculum design typically require domain-specific hyperparameter tuning or have limited theoretical underpinnings. To tackle these limitations, we design our curriculum strategy, ProCuRL, inspired by the pedagogical concept of Zone of Proximal Development (ZPD). ProCuRL captures the intuition that learning progress is maximized when picking tasks that are neither too hard nor too easy for the learner. We mathematically derive ProCuRL by analyzing two simple learning settings. We also present a practical variant of ProCuRL that can be directly integrated with deep RL frameworks with minimal hyperparameter tuning. Experimental results on a variety of domains demonstrate the effectiveness of our curriculum strategy over state-of-the-art baselines in accelerating the training process of deep RL agents.

Andi Nika, Debmalya Mandal, Parameswaran Kamalaruban et al.

We consider robustness against data corruption in offline multi-agent reinforcement learning from human feedback (MARLHF) under a strong-contamination model: given a dataset $D$ of trajectory-preference tuples (each preference being an $n$-dimensional binary label vector representing each of the $n$ agents' preferences), an $ε$-fraction of the samples may be arbitrarily corrupted. We model the problem using the framework of linear Markov games. First, under a uniform coverage assumption - where every policy of interest is sufficiently represented in the clean (prior to corruption) data - we introduce a robust estimator that guarantees an $O(ε^{1 - o(1)})$ bound on the Nash equilibrium gap. Next, we move to the more challenging unilateral coverage setting, in which only a Nash equilibrium and its single-player deviations are covered. In this case, our proposed algorithm achieves an $O(\sqrtε)$ bound on the Nash gap. Both of these procedures, however, suffer from intractable computation. To address this, we relax our solution concept to coarse correlated equilibria (CCE). Under the same unilateral coverage regime, we derive a quasi-polynomial-time algorithm whose CCE gap scales as $O(\sqrtε)$. To the best of our knowledge, this is the first systematic treatment of adversarial data corruption in offline MARLHF.

Xiaohang Tang, Afonso Marques, Parameswaran Kamalaruban et al.

Decision Transformer (DT), as one of the representative Reinforcement Learning via Supervised Learning (RvS) methods, has achieved strong performance in offline learning tasks by leveraging the powerful Transformer architecture for sequential decision-making. However, in adversarial environments, these methods can be non-robust, since the return is dependent on the strategies of both the decision-maker and adversary. Training a probabilistic model conditioned on observed return to predict action can fail to generalize, as the trajectories that achieve a return in the dataset might have done so due to a suboptimal behavior adversary. To address this, we propose a worst-case-aware RvS algorithm, the Adversarially Robust Decision Transformer (ARDT), which learns and conditions the policy on in-sample minimax returns-to-go. ARDT aligns the target return with the worst-case return learned through minimax expectile regression, thereby enhancing robustness against powerful test-time adversaries. In experiments conducted on sequential games with full data coverage, ARDT can generate a maximin (Nash Equilibrium) strategy, the solution with the largest adversarial robustness. In large-scale sequential games and continuous adversarial RL environments with partial data coverage, ARDT demonstrates significantly superior robustness to powerful test-time adversaries and attains higher worst-case returns compared to contemporary DT methods.

Victor-Alexandru Pădurean, Parameswaran Kamalaruban, Nachiket Kotalwar et al.

We study the problem of aligning a generative model's response with a user's preferences. Recent works have proposed several different formulations for personalized alignment; however, they either require a large amount of user preference queries or require that the preference be explicitly specified as a text input. In this paper, we propose a novel inference-time personalized alignment method, UserAlign, that elicits the user's preferences with a few queries as pairwise response comparisons. In particular, UserAlign builds on the theoretical framework of best-arm identification in logistic bandits and selects a personalized response from a fixed pool of the model's generated responses. The key idea is to consider the user's feedback consistent and noise-free, and incorporate it into the theoretical framework to identify the best response quickly. Experimental results across several tasks, involving personalized text and image generation, showcase the effectiveness of UserAlign in achieving personalized alignment.

Georgios Tzannetos, Parameswaran Kamalaruban, Adish Singla

Training agents to operate under strict constraints during deployment, such as limited resource budgets or stringent safety requirements, presents significant challenges, especially when these constraints render the task complex. In this work, we propose a curriculum learning strategy that gradually tightens constraints during training, enabling the agent to incrementally master the deployment requirements. Inspired by self-paced learning techniques in unconstrained reinforcement learning (RL), our approach facilitates a smoother transition to challenging environments by initially training on simplified versions of the constraints and progressively introducing the full deployment conditions. We provide a theoretical analysis using an RL agent in a binary-tree Markov Decision Process (MDP) to demonstrate that our curriculum strategy can accelerate training relative to a baseline approach that imposes the trajectory constraints from the outset. Moreover, we empirically validate the effectiveness and generality of our method across both RL and large language model (LLM) agents in diverse settings, including a binary-tree MDP, a multi-task navigation domain, and a math reasoning task with two benchmarks. These results highlight the potential of curriculum design in enhancing the efficiency and performance of agents operating under complex trajectory constraints during deployment. Moreover, when applied to LLMs, our strategy enables compression of output chain-of-thought tokens, achieving a substantial inference speedup on consumer hardware, demonstrating its effectiveness for resource-constrained deployment.

Parameswaran Kamalaruban, Yulu Pi, Stuart Burrell et al.

Ensuring fairness in transaction fraud detection models is vital due to the potential harms and legal implications of biased decision-making. Despite extensive research on algorithmic fairness, there is a notable gap in the study of bias in fraud detection models, mainly due to the field's unique challenges. These challenges include the need for fairness metrics that account for fraud data's imbalanced nature and the tradeoff between fraud protection and service quality. To address this gap, we present a comprehensive fairness evaluation of transaction fraud models using public synthetic datasets, marking the first algorithmic bias audit in this domain. Our findings reveal three critical insights: (1) Certain fairness metrics expose significant bias only after normalization, highlighting the impact of class imbalance. (2) Bias is significant in both service quality-related parity metrics and fraud protection-related parity metrics. (3) The fairness through unawareness approach, which involved removing sensitive attributes such as gender, does not improve bias mitigation within these datasets, likely due to the presence of correlated proxies. We also discuss socio-technical fairness-related challenges in transaction fraud models. These insights underscore the need for a nuanced approach to fairness in fraud detection, balancing protection and service quality, and moving beyond simple bias mitigation strategies. Future work must focus on refining fairness metrics and developing methods tailored to the unique complexities of the transaction fraud domain.

Tom Kempton, Julia Rozanova, Parameswaran Kamalaruban et al.

Large Language Models (LLMs) are a powerful tool for statistical text analysis, with derived sequences of next-token probability distributions offering a wealth of information. Extracting this signal typically relies on metrics such as perplexity, which do not adequately account for context; how one should interpret a given next-token probability is dependent on the number of reasonable choices encoded by the shape of the conditional distribution. In this work, we present DMAP, a mathematically grounded method that maps a text, via a language model, to a set of samples in the unit interval that jointly encode rank and probability information. This representation enables efficient, model-agnostic analysis and supports a range of applications. We illustrate its utility through three case studies: (i) validation of generation parameters to ensure data integrity, (ii) examining the role of probability curvature in machine-generated text detection, and (iii) a forensic analysis revealing statistical fingerprints left in downstream models that have been subject to post-training on synthetic data. Our results demonstrate that DMAP offers a unified statistical view of text that is simple to compute on consumer hardware, widely applicable, and provides a foundation for further research into text analysis with LLMs.

Maeve Madigan, Parameswaran Kamalaruban, Glenn Moynihan et al.

Multi-agent systems have demonstrated the ability to improve performance on a variety of predictive tasks by leveraging collaborative decision making. However, the lack of effective evaluation methodologies has made it difficult to estimate the risk of bias, making deployment of such systems unsafe in high stakes domains such as consumer finance, where biased decisions can translate directly into regulatory breaches and financial loss. To address this challenge, we need to develop fairness evaluation methodologies for multi-agent predictive systems and measure the fairness characteristics of these systems in the financial tabular domain. Examining fairness metrics using large-scale simulations across diverse multi-agent configurations, with varying communication and collaboration mechanisms, we reveal patterns of emergent bias in financial decision-making that cannot be traced to individual agent components, indicating that multi-agent systems may exhibit genuinely collective behaviors. Our findings highlight that fairness risks in financial multi-agent systems represent a significant component of model risk, with tangible impacts on tasks such as credit scoring and income estimation. We advocate that multi-agent decision systems must be evaluated as holistic entities rather than through reductionist analyses of their constituent components.

Andi Nika, Debmalya Mandal, Parameswaran Kamalaruban et al.

In this paper, we take a step towards a deeper understanding of learning from human preferences by systematically comparing the paradigm of reinforcement learning from human feedback (RLHF) with the recently proposed paradigm of direct preference optimization (DPO). We focus our attention on the class of loglinear policy parametrization and linear reward functions. In order to compare the two paradigms, we first derive minimax statistical bounds on the suboptimality gap induced by both RLHF and DPO, assuming access to an oracle that exactly solves the optimization problems. We provide a detailed discussion on the relative comparison between the two paradigms, simultaneously taking into account the sample size, policy and reward class dimensions, and the regularization temperature. Moreover, we extend our analysis to the approximate optimization setting and derive exponentially decaying convergence rates for both RLHF and DPO. Next, we analyze the setting where the ground-truth reward is not realizable and find that, while RLHF incurs a constant additional error, DPO retains its asymptotically decaying gap by just tuning the temperature accordingly. Finally, we extend our comparison to the Markov decision process setting, where we generalize our results with exact optimization. To the best of our knowledge, we are the first to provide such a comparative analysis for RLHF and DPO.

Debmalya Mandal, Andi Nika, Parameswaran Kamalaruban et al.

We study data corruption robustness for reinforcement learning with human feedback (RLHF) in an offline setting. Given an offline dataset of pairs of trajectories along with feedback about human preferences, an $\varepsilon$-fraction of the pairs is corrupted (e.g., feedback flipped or trajectory features manipulated), capturing an adversarial attack or noisy human preferences. We aim to design algorithms that identify a near-optimal policy from the corrupted data, with provable guarantees. Existing theoretical works have separately studied the settings of corruption robust RL (learning from scalar rewards directly under corruption) and offline RLHF (learning from human feedback without corruption); however, they are inapplicable to our problem of dealing with corrupted data in offline RLHF setting. To this end, we design novel corruption robust offline RLHF methods under various assumptions on the coverage of the data-generating distributions. At a high level, our methodology robustifies an offline RLHF framework by first learning a reward model along with confidence sets and then learning a pessimistic optimal policy over the confidence set. Our key insight is that learning optimal policy can be done by leveraging an offline corruption-robust RL oracle in different ways (e.g., zero-order oracle or first-order oracle), depending on the data coverage assumptions. To our knowledge, ours is the first work that provides provable corruption robust offline RLHF methods.

Georgios Tzannetos, Parameswaran Kamalaruban, Adish Singla

Curriculum design for reinforcement learning (RL) can speed up an agent's learning process and help it learn to perform well on complex tasks. However, existing techniques typically require domain-specific hyperparameter tuning, involve expensive optimization procedures for task selection, or are suitable only for specific learning objectives. In this work, we consider curriculum design in contextual multi-task settings where the agent's final performance is measured w.r.t. a target distribution over complex tasks. We base our curriculum design on the Zone of Proximal Development concept, which has proven to be effective in accelerating the learning process of RL agents for uniform distribution over all tasks. We propose a novel curriculum, ProCuRL-Target, that effectively balances the need for selecting tasks that are not too difficult for the agent while progressing the agent's learning toward the target distribution via leveraging task correlations. We theoretically justify the task selection strategy of ProCuRL-Target by analyzing a simple learning setting with REINFORCE learner model. Our experimental results across various domains with challenging target task distributions affirm the effectiveness of our curriculum strategy over state-of-the-art baselines in accelerating the training process of deep RL agents.

Rati Devidze, Parameswaran Kamalaruban, Adish Singla

Reward functions are central in specifying the task we want a reinforcement learning agent to perform. Given a task and desired optimal behavior, we study the problem of designing informative reward functions so that the designed rewards speed up the agent's convergence. In particular, we consider expert-driven reward design settings where an expert or teacher seeks to provide informative and interpretable rewards to a learning agent. Existing works have considered several different reward design formulations; however, the key challenge is formulating a reward informativeness criterion that adapts w.r.t. the agent's current policy and can be optimized under specified structural constraints to obtain interpretable rewards. In this paper, we propose a novel reward informativeness criterion, a quantitative measure that captures how the agent's current policy will improve if it receives rewards from a specific reward function. We theoretically showcase the utility of the proposed informativeness criterion for adaptively designing rewards for an agent. Experimental results on two navigation tasks demonstrate the effectiveness of our adaptive reward informativeness criterion.

Andi Nika, Jonathan Nöther, Debmalya Mandal et al.

We study data poisoning attacks in learning from human preferences. More specifically, we consider the problem of teaching/enforcing a target policy $π^\dagger$ by synthesizing preference data. We seek to understand the susceptibility of different preference-based learning paradigms to poisoned preference data by analyzing the number of samples required by the attacker to enforce $π^\dagger$. We first propose a general data poisoning formulation in learning from human preferences and then study it for two popular paradigms, namely: (a) reinforcement learning from human feedback (RLHF) that operates by learning a reward model using preferences; (b) direct preference optimization (DPO) that directly optimizes policy using preferences. We conduct a theoretical analysis of the effectiveness of data poisoning in a setting where the attacker is allowed to augment a pre-existing dataset and also study its special case where the attacker can synthesize the entire preference dataset from scratch. As our main results, we provide lower/upper bounds on the number of samples required to enforce $π^\dagger$. Finally, we discuss the implications of our results in terms of the susceptibility of these learning paradigms under such data poisoning attacks.

Parameswaran Kamalaruban, Mark Anderson, Stuart Burrell et al.

Pre-trained foundation models can be adapted for specific tasks using Low-Rank Adaptation (LoRA). However, the fairness properties of these adapted classifiers remain underexplored. Existing fairness-aware fine-tuning methods rely on direct access to sensitive attributes or their predictors, but in practice, these sensitive attributes are often held under strict consumer privacy controls, and neither the attributes nor their predictors are available to model developers, hampering the development of fair models. To address this issue, we introduce a set of LoRA-based fine-tuning methods that can be trained in a distributed fashion, where model developers and fairness auditors collaborate without sharing sensitive attributes or predictors. In this paper, we evaluate three such methods - sensitive unlearning, adversarial training, and orthogonality loss - against a fairness-unaware baseline, using experiments on the CelebA and UTK-Face datasets with an ImageNet pre-trained ViT-Base model. We find that orthogonality loss consistently reduces bias while maintaining or improving utility, whereas adversarial training improves False Positive Rate Parity and Demographic Parity in some cases, and sensitive unlearning provides no clear benefit. In tasks where significant biases are present, distributed fairness-aware fine-tuning methods can effectively eliminate bias without compromising consumer privacy and, in most cases, improve model utility.

Luca Viano, Yu-Ting Huang, Parameswaran Kamalaruban et al.

Imitation learning (IL) is a popular paradigm for training policies in robotic systems when specifying the reward function is difficult. However, despite the success of IL algorithms, they impose the somewhat unrealistic requirement that the expert demonstrations must come from the same domain in which a new imitator policy is to be learned. We consider a practical setting, where (i) state-only expert demonstrations from the real (deployment) environment are given to the learner, (ii) the imitation learner policy is trained in a simulation (training) environment whose transition dynamics is slightly different from the real environment, and (iii) the learner does not have any access to the real environment during the training phase beyond the batch of demonstrations given. Most of the current IL methods, such as generative adversarial imitation learning and its state-only variants, fail to imitate the optimal expert behavior under the above setting. By leveraging insights from the Robust reinforcement learning (RL) literature and building on recent adversarial imitation approaches, we propose a robust IL algorithm to learn policies that can effectively transfer to the real environment without fine-tuning. Furthermore, we empirically demonstrate on continuous-control benchmarks that our method outperforms the state-of-the-art state-only IL method in terms of the zero-shot transfer performance in the real environment and robust performance under different testing conditions.

Gaurav Yengera, Rati Devidze, Parameswaran Kamalaruban et al.

We consider the problem of teaching via demonstrations in sequential decision-making settings. In particular, we study how to design a personalized curriculum over demonstrations to speed up the learner's convergence. We provide a unified curriculum strategy for two popular learner models: Maximum Causal Entropy Inverse Reinforcement Learning (MaxEnt-IRL) and Cross-Entropy Behavioral Cloning (CrossEnt-BC). Our unified strategy induces a ranking over demonstrations based on a notion of difficulty scores computed w.r.t. the teacher's optimal policy and the learner's current policy. Compared to the state of the art, our strategy doesn't require access to the learner's internal dynamics and still enjoys similar convergence guarantees under mild technical conditions. Furthermore, we adapt our curriculum strategy to the setting where no teacher agent is present using task-specific difficulty scores. Experiments on a synthetic car driving environment and navigation-based environments demonstrate the effectiveness of our curriculum strategy.

Luca Viano, Yu-Ting Huang, Parameswaran Kamalaruban et al.

We study the inverse reinforcement learning (IRL) problem under a transition dynamics mismatch between the expert and the learner. Specifically, we consider the Maximum Causal Entropy (MCE) IRL learner model and provide a tight upper bound on the learner's performance degradation based on the $\ell_1$-distance between the transition dynamics of the expert and the learner. Leveraging insights from the Robust RL literature, we propose a robust MCE IRL algorithm, which is a principled approach to help with this mismatch. Finally, we empirically demonstrate the stable performance of our algorithm compared to the standard MCE IRL algorithm under transition dynamics mismatches in both finite and continuous MDP problems.

Martin Troussard, Emmanuel Pignat, Parameswaran Kamalaruban et al.

This paper proposes an inverse reinforcement learning (IRL) framework to accelerate learning when the learner-teacher \textit{interaction} is \textit{limited} during training. Our setting is motivated by the realistic scenarios where a helpful teacher is not available or when the teacher cannot access the learning dynamics of the student. We present two different training strategies: Curriculum Inverse Reinforcement Learning (CIRL) covering the teacher's perspective, and Self-Paced Inverse Reinforcement Learning (SPIRL) focusing on the learner's perspective. Using experiments in simulations and experiments with a real robot learning a task from a human demonstrator, we show that our training strategies can allow a faster training than a random teacher for CIRL and than a batch learner for SPIRL.

Parameswaran Kamalaruban, Rati Devidze, Volkan Cevher et al.

One of the central challenges faced by a reinforcement learning (RL) agent is to effectively learn a (near-)optimal policy in environments with large state spaces having sparse and noisy feedback signals. In real-world applications, an expert with additional domain knowledge can help in speeding up the learning process via \emph{shaping the environment}, i.e., making the environment more learner-friendly. A popular paradigm in literature is \emph{potential-based reward shaping}, where the environment's reward function is augmented with additional local rewards using a potential function. However, the applicability of potential-based reward shaping is limited in settings where (i) the state space is very large, and it is challenging to compute an appropriate potential function, (ii) the feedback signals are noisy, and even with shaped rewards the agent could be trapped in local optima, and (iii) changing the rewards alone is not sufficient, and effective shaping requires changing the dynamics. We address these limitations of potential-based shaping methods and propose a novel framework of \emph{environment shaping using state abstraction}. Our key idea is to compress the environment's large state space with noisy signals to an abstracted space, and to use this abstraction in creating smoother and more effective feedback signals for the agent. We study the theoretical underpinnings of our abstraction-based environment shaping, and show that the agent's policy learnt in the shaped environment preserves near-optimal behavior in the original environment.

Parameswaran Kamalaruban, Yu-Ting Huang, Ya-Ping Hsieh et al.

We introduce a sampling perspective to tackle the challenging task of training robust Reinforcement Learning (RL) agents. Leveraging the powerful Stochastic Gradient Langevin Dynamics, we present a novel, scalable two-player RL algorithm, which is a sampling variant of the two-player policy gradient method. Our algorithm consistently outperforms existing baselines, in terms of generalization across different training and testing conditions, on several MuJoCo environments. Our experiments also show that, even for objective functions that entirely ignore potential environmental shifts, our sampling approach remains highly robust in comparison to standard RL algorithms.

Donghwan Lee, Niao He, Parameswaran Kamalaruban et al.

This article reviews recent advances in multi-agent reinforcement learning algorithms for large-scale control systems and communication networks, which learn to communicate and cooperate. We provide an overview of this emerging field, with an emphasis on the decentralized setting under different coordination protocols. We highlight the evolution of reinforcement learning algorithms from single-agent to multi-agent systems, from a distributed optimization perspective, and conclude with future directions and challenges, in the hope to catalyze the growing synergy among distributed optimization, signal processing, and reinforcement learning communities.

Parameswaran Kamalaruban, Rati Devidze, Volkan Cevher et al.

We study the problem of inverse reinforcement learning (IRL) with the added twist that the learner is assisted by a helpful teacher. More formally, we tackle the following algorithmic question: How could a teacher provide an informative sequence of demonstrations to an IRL learner to speed up the learning process? We present an interactive teaching framework where a teacher adaptively chooses the next demonstration based on learner's current policy. In particular, we design teaching algorithms for two concrete settings: an omniscient setting where a teacher has full knowledge about the learner's dynamics and a blackbox setting where the teacher has minimal knowledge. Then, we study a sequential variant of the popular MCE-IRL learner and prove convergence guarantees of our teaching algorithm in the omniscient setting. Extensive experiments with a car driving simulator environment show that the learning progress can be speeded up drastically as compared to an uninformative teacher.

Teresa Yeo, Parameswaran Kamalaruban, Adish Singla et al.

We consider the machine teaching problem in a classroom-like setting wherein the teacher has to deliver the same examples to a diverse group of students. Their diversity stems from differences in their initial internal states as well as their learning rates. We prove that a teacher with full knowledge about the learning dynamics of the students can teach a target concept to the entire classroom using O(min{d,N} log(1/eps)) examples, where d is the ambient dimension of the problem, N is the number of learners, and eps is the accuracy parameter. We show the robustness of our teaching strategy when the teacher has limited knowledge of the learners' internal dynamics as provided by a noisy oracle. Further, we study the trade-off between the learners' workload and the teacher's cost in teaching the target concept. Our experiments validate our theoretical results and suggest that appropriately partitioning the classroom into homogenous groups provides a balance between these two objectives.

Parameswaran Kamalaruban, Victor Perrier, Hassan Jameel Asghar et al.

Differential privacy provides strong privacy guarantees simultaneously enabling useful insights from sensitive datasets. However, it provides the same level of protection for all elements (individuals and attributes) in the data. There are practical scenarios where some data attributes need more/less protection than others. In this paper, we consider $d_{\mathcal{X}}$-privacy, an instantiation of the privacy notion introduced in \cite{chatzikokolakis2013broadening}, which allows this flexibility by specifying a separate privacy budget for each pair of elements in the data domain. We describe a systematic procedure to tailor any existing differentially private mechanism that assumes a query set and a sensitivity vector as input into its $d_{\mathcal{X}}$-private variant, specifically focusing on linear queries. Our proposed meta procedure has broad applications as linear queries form the basis of a range of data analysis and machine learning algorithms, and the ability to define a more flexible privacy budget across the data domain results in improved privacy/utility tradeoff in these applications. We propose several $d_{\mathcal{X}}$-private mechanisms, and provide theoretical guarantees on the trade-off between utility and privacy. We also experimentally demonstrate the effectiveness of our procedure, by evaluating our proposed $d_{\mathcal{X}}$-private Laplace mechanism on both synthetic and real datasets using a set of randomly generated linear queries.

Parameswaran Kamalaruban

This thesis presents some geometric insights into three different types of two player prediction games -- namely general learning task, prediction with expert advice, and online convex optimization. These games differ in the nature of the opponent (stochastic, adversarial, or intermediate), the order of the players' move, and the utility function. The insights shed some light on the understanding of the intrinsic barriers of the prediction problems and the design of computationally efficient learning algorithms with strong theoretical guarantees (such as generalizability, statistical consistency, and constant regret etc.).

Parameswaran Kamalaruban, Robert C. Williamson, Xinhua Zhang

The goal of online prediction with expert advice is to find a decision strategy which will perform almost as well as the best expert in a given pool of experts, on any sequence of outcomes. This problem has been widely studied and $O(\sqrt{T})$ and $O(\log{T})$ regret bounds can be achieved for convex losses (\cite{zinkevich2003online}) and strictly convex losses with bounded first and second derivatives (\cite{hazan2007logarithmic}) respectively. In special cases like the Aggregating Algorithm (\cite{vovk1995game}) with mixable losses and the Weighted Average Algorithm (\cite{kivinen1999averaging}) with exp-concave losses, it is possible to achieve $O(1)$ regret bounds. \cite{van2012exp} has argued that mixability and exp-concavity are roughly equivalent under certain conditions. Thus by understanding the underlying relationship between these two notions we can gain the best of both algorithms (strong theoretical performance guarantees of the Aggregating Algorithm and the computational efficiency of the Weighted Average Algorithm). In this paper we provide a complete characterization of the exp-concavity of any proper composite loss. Using this characterization and the mixability condition of proper losses (\cite{van2012mixability}), we show that it is possible to transform (re-parameterize) any $β$-mixable binary proper loss into a $β$-exp-concave composite loss with the same $β$. In the multi-class case, we propose an approximation approach for this transformation.

Parameswaran Kamalaruban, Robert C. Williamson

The cost-sensitive classification problem plays a crucial role in mission-critical machine learning applications, and differs with traditional classification by taking the misclassification costs into consideration. Although being studied extensively in the literature, the fundamental limits of this problem are still not well understood. We investigate the hardness of this problem by extending the standard minimax lower bound of balanced binary classification problem (due to \cite{massart2006risk}), and emphasize the impact of cost terms on the hardness.

Parameswaran Kamalaruban

Online Convex Optimization plays a key role in large scale machine learning. Early approaches to this problem were conservative, in which the main focus was protection against the worst case scenario. But recently several algorithms have been developed for tightening the regret bounds in easy data instances such as sparsity, predictable sequences, and curved losses. In this work we unify some of these existing techniques to obtain new update rules for the cases when these easy instances occur together. First we analyse an adaptive and optimistic update rule which achieves tighter regret bound when the loss sequence is sparse and predictable. Then we explain an update rule that dynamically adapts to the curvature of the loss function and utilizes the predictable nature of the loss sequence as well. Finally we extend these results to composite losses.

Kush Bhatia, Prateek Jain, Parameswaran Kamalaruban et al.

We study the problem of robust time series analysis under the standard auto-regressive (AR) time series model in the presence of arbitrary outliers. We devise an efficient hard thresholding based algorithm which can obtain a consistent estimate of the optimal AR model despite a large fraction of the time series points being corrupted. Our algorithm alternately estimates the corrupted set of points and the model parameters, and is inspired by recent advances in robust regression and hard-thresholding methods. However, a direct application of existing techniques is hindered by a critical difference in the time-series domain: each point is correlated with all previous points rendering existing tools inapplicable directly. We show how to overcome this hurdle using novel proof techniques. Using our techniques, we are also able to provide the first efficient and provably consistent estimator for the robust regression problem where a standard linear observation model with white additive noise is corrupted arbitrarily. We illustrate our methods on synthetic datasets and show that our methods indeed are able to consistently recover the optimal parameters despite a large fraction of points being corrupted.