arXiv subjects

Aadirupa Saha

Publications and source records attributed to Aadirupa Saha.

At least 37 records · Page 2Linked to original sources

arXiv2023

Dueling RL: Reinforcement Learning with Trajectory Preferences

We consider the problem of preference based reinforcement learning (PbRL), where, unlike traditional reinforcement learning, an agent receives feedback only in terms of a 1 bit (0/1) preference over a trajectory pair instead of absolute rewards for them. The success of the traditional RL framework crucially relies on the underlying agent-reward model, which, however, depends on how accurately a system designer can express an appropriate reward function and often a non-trivial task. The main novelty of our framework is the ability to learn from preference-based trajectory feedback that eliminates the need to hand-craft numeric reward models. This paper sets up a formal framework for the PbRL problem with non-markovian rewards, where the trajectory preferences are encoded by a generalized linear model of dimension $d$. Assuming the transition model is known, we then propose an algorithm with almost optimal regret guarantee of $\tilde {\mathcal{O}}\left( SH d \log (T / δ) \sqrt{T} \right)$. We further, extend the above algorithm to the case of unknown transition dynamics, and provide an algorithm with near optimal regret guarantee $\widetilde{\mathcal{O}}((\sqrt{d} + H^2 + |\mathcal{S}|)\sqrt{dT} +\sqrt{|\mathcal{S}||\mathcal{A}|TH} )$. To the best of our knowledge, our work is one of the first to give tight regret guarantees for preference based RL problems with trajectory preferences.

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arXiv2022

One Arrow, Two Kills: An Unified Framework for Achieving Optimal Regret Guarantees in Sleeping Bandits

We address the problem of \emph{`Internal Regret'} in \emph{Sleeping Bandits} in the fully adversarial setup, as well as draw connections between different existing notions of sleeping regrets in the multiarmed bandits (MAB) literature and consequently analyze the implications: Our first contribution is to propose the new notion of \emph{Internal Regret} for sleeping MAB. We then proposed an algorithm that yields sublinear regret in that measure, even for a completely adversarial sequence of losses and availabilities. We further show that a low sleeping internal regret always implies a low external regret, and as well as a low policy regret for iid sequence of losses. The main contribution of this work precisely lies in unifying different notions of existing regret in sleeping bandits and understand the implication of one to another. Finally, we also extend our results to the setting of \emph{Dueling Bandits} (DB)--a preference feedback variant of MAB, and proposed a reduction to MAB idea to design a low regret algorithm for sleeping dueling bandits with stochastic preferences and adversarial availabilities. The efficacy of our algorithms is justified through empirical evaluations.

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arXiv2022

ANACONDA: An Improved Dynamic Regret Algorithm for Adaptive Non-Stationary Dueling Bandits

We study the problem of non-stationary dueling bandits and provide the first adaptive dynamic regret algorithm for this problem. The only two existing attempts in this line of work fall short across multiple dimensions, including pessimistic measures of non-stationary complexity and non-adaptive parameter tuning that requires knowledge of the number of preference changes. We develop an elimination-based rescheduling algorithm to overcome these shortcomings and show a near-optimal $\tilde{O}(\sqrt{S^{\texttt{CW}} T})$ dynamic regret bound, where $S^{\texttt{CW}}$ is the number of times the Condorcet winner changes in $T$ rounds. This yields the first near-optimal dynamic regret algorithm for unknown $S^{\texttt{CW}}$. We further study other related notions of non-stationarity for which we also prove near-optimal dynamic regret guarantees under additional assumptions on the underlying preference model.

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arXiv2022

Stochastic Contextual Dueling Bandits under Linear Stochastic Transitivity Models

We consider the regret minimization task in a dueling bandits problem with context information. In every round of the sequential decision problem, the learner makes a context-dependent selection of two choice alternatives (arms) to be compared with each other and receives feedback in the form of noisy preference information. We assume that the feedback process is determined by a linear stochastic transitivity model with contextualized utilities (CoLST), and the learner's task is to include the best arm (with highest latent context-dependent utility) in the duel. We propose a computationally efficient algorithm, $\texttt{CoLSTIM}$, which makes its choice based on imitating the feedback process using perturbed context-dependent utility estimates of the underlying CoLST model. If each arm is associated with a $d$-dimensional feature vector, we show that $\texttt{CoLSTIM}$ achieves a regret of order $\tilde O( \sqrt{dT})$ after $T$ learning rounds. Additionally, we also establish the optimality of $\texttt{CoLSTIM}$ by showing a lower bound for the weak regret that refines the existing average regret analysis. Our experiments demonstrate its superiority over state-of-art algorithms for special cases of CoLST models.

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arXiv2022

Dueling Convex Optimization with General Preferences

We address the problem of \emph{convex optimization with dueling feedback}, where the goal is to minimize a convex function given a weaker form of \emph{dueling} feedback. Each query consists of two points and the dueling feedback returns a (noisy) single-bit binary comparison of the function values of the two queried points. The translation of the function values to the single comparison bit is through a \emph{transfer function}. This problem has been addressed previously for some restricted classes of transfer functions, but here we consider a very general transfer function class which includes all functions that can be approximated by a finite polynomial with a minimal degree $p$. Our main contribution is an efficient algorithm with convergence rate of $\smash{\widetilde O}(ε^{-4p})$ for a smooth convex objective function, and an optimal rate of $\smash{\widetilde O}(ε^{-2p})$ when the objective is smooth and strongly convex.

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arXiv2022

Optimal and Efficient Dynamic Regret Algorithms for Non-Stationary Dueling Bandits

We study the problem of \emph{dynamic regret minimization} in $K$-armed Dueling Bandits under non-stationary or time varying preferences. This is an online learning setup where the agent chooses a pair of items at each round and observes only a relative binary `win-loss' feedback for this pair, sampled from an underlying preference matrix at that round. We first study the problem of static-regret minimization for adversarial preference sequences and design an efficient algorithm with $O(\sqrt{KT})$ high probability regret. We next use similar algorithmic ideas to propose an efficient and provably optimal algorithm for dynamic-regret minimization under two notions of non-stationarities. In particular, we establish $\tO(\sqrt{SKT})$ and $\tO({V_T^{1/3}K^{1/3}T^{2/3}})$ dynamic-regret guarantees, $S$ being the total number of `effective-switches' in the underlying preference relations and $V_T$ being a measure of `continuous-variation' non-stationarity. The complexity of these problems have not been studied prior to this work despite the practicability of non-stationary environments in real world systems. We justify the optimality of our algorithms by proving matching lower bound guarantees under both the above-mentioned notions of non-stationarities. Finally, we corroborate our results with extensive simulations and compare the efficacy of our algorithms over state-of-the-art baselines.

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arXiv2022

Exploiting Correlation to Achieve Faster Learning Rates in Low-Rank Preference Bandits

We introduce the \emph{Correlated Preference Bandits} problem with random utility-based choice models (RUMs), where the goal is to identify the best item from a given pool of $n$ items through online subsetwise preference feedback. We investigate whether models with a simple correlation structure, e.g. low rank, can result in faster learning rates. While we show that the problem can be impossible to solve for the general `low rank' choice models, faster learning rates can be attained assuming more structured item correlations. In particular, we introduce a new class of \emph{Block-Rank} based RUM model, where the best item is shown to be $(ε,δ)$-PAC learnable with only $O(r ε^{-2} \log(n/δ))$ samples. This improves on the standard sample complexity bound of $\tilde{O}(nε^{-2} \log(1/δ))$ known for the usual learning algorithms which might not exploit the item-correlations ($r \ll n$). We complement the above sample complexity with a matching lower bound (up to logarithmic factors), justifying the tightness of our analysis. Surprisingly, we also show a lower bound of $Ω(nε^{-2}\log(1/δ))$ when the learner is forced to play just duels instead of larger subsetwise queries. Further, we extend the results to a more general `\emph{noisy Block-Rank}' model, which ensures robustness of our techniques. Overall, our results justify the advantage of playing subsetwise queries over pairwise preferences $(k=2)$, we show the latter provably fails to exploit correlation.

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arXiv2022

Versatile Dueling Bandits: Best-of-both-World Analyses for Online Learning from Preferences

We study the problem of $K$-armed dueling bandit for both stochastic and adversarial environments, where the goal of the learner is to aggregate information through relative preferences of pair of decisions points queried in an online sequential manner. We first propose a novel reduction from any (general) dueling bandits to multi-armed bandits and despite the simplicity, it allows us to improve many existing results in dueling bandits. In particular, \emph{we give the first best-of-both world result for the dueling bandits regret minimization problem} -- a unified framework that is guaranteed to perform optimally for both stochastic and adversarial preferences simultaneously. Moreover, our algorithm is also the first to achieve an optimal $O(\sum_{i = 1}^K \frac{\log T}{Δ_i})$ regret bound against the Condorcet-winner benchmark, which scales optimally both in terms of the arm-size $K$ and the instance-specific suboptimality gaps $\{Δ_i\}_{i = 1}^K$. This resolves the long-standing problem of designing an instancewise gap-dependent order optimal regret algorithm for dueling bandits (with matching lower bounds up to small constant factors). We further justify the robustness of our proposed algorithm by proving its optimal regret rate under adversarially corrupted preferences -- this outperforms the existing state-of-the-art corrupted dueling results by a large margin. In summary, we believe our reduction idea will find a broader scope in solving a diverse class of dueling bandits setting, which are otherwise studied separately from multi-armed bandits with often more complex solutions and worse guarantees. The efficacy of our proposed algorithms is empirically corroborated against the existing dueling bandit methods.

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arXiv2021

A Sketch Based Game Theoretic Approach to Detect Anomalous Dense Sub-Communities in Large Data Streams

Detecting anomalous subgraphs in a dynamic graph in an online or streaming fashion is an important requirement in industrial settings for intrusion detection or denial of service attacks. While only detecting anomalousness in the system by edge frequencies is an optimal approach, many latent information can get unnoticed in the process, since as a characteristic of the network only edge frequencies are considered. We propose a game theoretic approach whereby using the modularity function we try to estimate in a streaming graph \emph{whether addition of a new edge in the current time tick results in a dense subgraph creation, thus indicating possible anomalous score}. Our contributions are as follows: (a) We propose a novel game-theoretic framework for detecting dense subcommunities in an online streaming environment; (b) We detect such subcommunities using constant memory storage. Our results are corroborated with empirical evaluation on real datasets.

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arXiv2021

Efficient and Optimal Algorithms for Contextual Dueling Bandits under Realizability

We study the $K$-armed contextual dueling bandit problem, a sequential decision making setting in which the learner uses contextual information to make two decisions, but only observes \emph{preference-based feedback} suggesting that one decision was better than the other. We focus on the regret minimization problem under realizability, where the feedback is generated by a pairwise preference matrix that is well-specified by a given function class $\mathcal F$. We provide a new algorithm that achieves the optimal regret rate for a new notion of best response regret, which is a strictly stronger performance measure than those considered in prior works. The algorithm is also computationally efficient, running in polynomial time assuming access to an online oracle for square loss regression over $\mathcal F$. This resolves an open problem of Dudík et al. [2015] on oracle efficient, regret-optimal algorithms for contextual dueling bandits.

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arXiv2021

Strategically Efficient Exploration in Competitive Multi-agent Reinforcement Learning

High sample complexity remains a barrier to the application of reinforcement learning (RL), particularly in multi-agent systems. A large body of work has demonstrated that exploration mechanisms based on the principle of optimism under uncertainty can significantly improve the sample efficiency of RL in single agent tasks. This work seeks to understand the role of optimistic exploration in non-cooperative multi-agent settings. We will show that, in zero-sum games, optimistic exploration can cause the learner to waste time sampling parts of the state space that are irrelevant to strategic play, as they can only be reached through cooperation between both players. To address this issue, we introduce a formal notion of strategically efficient exploration in Markov games, and use this to develop two strategically efficient learning algorithms for finite Markov games. We demonstrate that these methods can be significantly more sample efficient than their optimistic counterparts.

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arXiv2021

Confidence-Budget Matching for Sequential Budgeted Learning

A core element in decision-making under uncertainty is the feedback on the quality of the performed actions. However, in many applications, such feedback is restricted. For example, in recommendation systems, repeatedly asking the user to provide feedback on the quality of recommendations will annoy them. In this work, we formalize decision-making problems with querying budget, where there is a (possibly time-dependent) hard limit on the number of reward queries allowed. Specifically, we consider multi-armed bandits, linear bandits, and reinforcement learning problems. We start by analyzing the performance of `greedy' algorithms that query a reward whenever they can. We show that in fully stochastic settings, doing so performs surprisingly well, but in the presence of any adversity, this might lead to linear regret. To overcome this issue, we propose the Confidence-Budget Matching (CBM) principle that queries rewards when the confidence intervals are wider than the inverse square root of the available budget. We analyze the performance of CBM based algorithms in different settings and show that they perform well in the presence of adversity in the contexts, initial states, and budgets.

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arXiv2021

Dueling Bandits with Adversarial Sleeping

We introduce the problem of sleeping dueling bandits with stochastic preferences and adversarial availabilities (DB-SPAA). In almost all dueling bandit applications, the decision space often changes over time; eg, retail store management, online shopping, restaurant recommendation, search engine optimization, etc. Surprisingly, this `sleeping aspect' of dueling bandits has never been studied in the literature. Like dueling bandits, the goal is to compete with the best arm by sequentially querying the preference feedback of item pairs. The non-triviality however results due to the non-stationary item spaces that allow any arbitrary subsets items to go unavailable every round. The goal is to find an optimal `no-regret' policy that can identify the best available item at each round, as opposed to the standard `fixed best-arm regret objective' of dueling bandits. We first derive an instance-specific lower bound for DB-SPAA $Ω( \sum_{i =1}^{K-1}\sum_{j=i+1}^K \frac{\log T}{Δ(i,j)})$, where $K$ is the number of items and $Δ(i,j)$ is the gap between items $i$ and $j$. This indicates that the sleeping problem with preference feedback is inherently more difficult than that for classical multi-armed bandits (MAB). We then propose two algorithms, with near optimal regret guarantees. Our results are corroborated empirically.

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arXiv2021

Regret Minimization in Stochastic Contextual Dueling Bandits

We consider the problem of stochastic $K$-armed dueling bandit in the contextual setting, where at each round the learner is presented with a context set of $K$ items, each represented by a $d$-dimensional feature vector, and the goal of the learner is to identify the best arm of each context sets. However, unlike the classical contextual bandit setup, our framework only allows the learner to receive item feedback in terms of their (noisy) pariwise preferences--famously studied as dueling bandits which is practical interests in various online decision making scenarios, e.g. recommender systems, information retrieval, tournament ranking, where it is easier to elicit the relative strength of the items instead of their absolute scores. However, to the best of our knowledge this work is the first to consider the problem of regret minimization of contextual dueling bandits for potentially infinite decision spaces and gives provably optimal algorithms along with a matching lower bound analysis. We present two algorithms for the setup with respective regret guarantees $\tilde O(d\sqrt{T})$ and $\tilde O(\sqrt{dT \log K})$. Subsequently we also show that $Ω(\sqrt {dT})$ is actually the fundamental performance limit for this problem, implying the optimality of our second algorithm. However the analysis of our first algorithm is comparatively simpler, and it is often shown to outperform the former empirically. Finally, we corroborate all the theoretical results with suitable experiments.

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arXiv2021

Pure Exploration with Structured Preference Feedback

We consider the problem of pure exploration with subset-wise preference feedback, which contains $N$ arms with features. The learner is allowed to query subsets of size $K$ and receives feedback in the form of a noisy winner. The goal of the learner is to identify the best arm efficiently using as few queries as possible. This setting is relevant in various online decision-making scenarios involving human feedback such as online retailing, streaming services, news feed, and online advertising; since it is easier and more reliable for people to choose a preferred item from a subset than to assign a likability score to an item in isolation. To the best of our knowledge, this is the first work that considers the subset-wise preference feedback model in a structured setting, which allows for potentially infinite set of arms. We present two algorithms that guarantee the detection of the best-arm in $\tilde{O} (\frac{d^2}{K Δ^2})$ samples with probability at least $1 - δ$, where $d$ is the dimension of the arm-features and $Δ$ is the appropriate notion of utility gap among the arms. We also derive an instance-dependent lower bound of $Ω(\frac{d}{Δ^2} \log \frac{1}δ)$ which matches our upper bound on a worst-case instance. Finally, we run extensive experiments to corroborate our theoretical findings, and observe that our adaptive algorithm stops and requires up to 12x fewer samples than a non-adaptive algorithm.

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arXiv2021

Optimal Regret Algorithm for Pseudo-1d Bandit Convex Optimization

We study online learning with bandit feedback (i.e. learner has access to only zeroth-order oracle) where cost/reward functions $\f_t$ admit a "pseudo-1d" structure, i.e. $\f_t(\w) = \loss_t(\pred_t(\w))$ where the output of $\pred_t$ is one-dimensional. At each round, the learner observes context $\x_t$, plays prediction $\pred_t(\w_t; \x_t)$ (e.g. $\pred_t(\cdot)=\langle \x_t, \cdot\rangle$) for some $\w_t \in \mathbb{R}^d$ and observes loss $\loss_t(\pred_t(\w_t))$ where $\loss_t$ is a convex Lipschitz-continuous function. The goal is to minimize the standard regret metric. This pseudo-1d bandit convex optimization problem (\SBCO) arises frequently in domains such as online decision-making or parameter-tuning in large systems. For this problem, we first show a lower bound of $\min(\sqrt{dT}, T^{3/4})$ for the regret of any algorithm, where $T$ is the number of rounds. We propose a new algorithm \sbcalg that combines randomized online gradient descent with a kernelized exponential weights method to exploit the pseudo-1d structure effectively, guaranteeing the {\em optimal} regret bound mentioned above, up to additional logarithmic factors. In contrast, applying state-of-the-art online convex optimization methods leads to $\tilde{O}\left(\min\left(d^{9.5}\sqrt{T},\sqrt{d}T^{3/4}\right)\right)$ regret, that is significantly suboptimal in $d$.

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arXiv2021

Ranking with Features: Algorithm and A Graph Theoretic Analysis

We consider the problem of ranking a set of items from pairwise comparisons in the presence of features associated with the items. Recent works have established that $O(n\log(n))$ samples are needed to rank well when there is no feature information present. However, this might be sub-optimal in the presence of associated features. We introduce a new probabilistic preference model called feature-Bradley-Terry-Luce (f-BTL) model that generalizes the standard BTL model to incorporate feature information. We present a new least squares based algorithm called fBTL-LS which we show requires much lesser than $O(n\log(n))$ pairs to obtain a good ranking -- precisely our new sample complexity bound is of $O(α\log α)$, where $α$ denotes the number of `independent items' of the set, in general $α<< n$. Our analysis is novel and makes use of tools from classical graph matching theory to provide tighter bounds that sheds light on the true complexity of the ranking problem, capturing the item dependencies in terms of their feature representations. This was not possible with earlier matrix completion based tools used for this problem. We also prove an information theoretic lower bound on the required sample complexity for recovering the underlying ranking, which essentially shows the tightness of our proposed algorithms. The efficacy of our proposed algorithms are validated through extensive experimental evaluations on a variety of synthetic and real world datasets.

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arXiv2020

Adversarial Dueling Bandits

We introduce the problem of regret minimization in Adversarial Dueling Bandits. As in classic Dueling Bandits, the learner has to repeatedly choose a pair of items and observe only a relative binary `win-loss' feedback for this pair, but here this feedback is generated from an arbitrary preference matrix, possibly chosen adversarially. Our main result is an algorithm whose $T$-round regret compared to the \emph{Borda-winner} from a set of $K$ items is $\tilde{O}(K^{1/3}T^{2/3})$, as well as a matching $Ω(K^{1/3}T^{2/3})$ lower bound. We also prove a similar high probability regret bound. We further consider a simpler \emph{fixed-gap} adversarial setup, which bridges between two extreme preference feedback models for dueling bandits: stationary preferences and an arbitrary sequence of preferences. For the fixed-gap adversarial setup we give an $\smash{ \tilde{O}((K/Δ^2)\log{T}) }$ regret algorithm, where $Δ$ is the gap in Borda scores between the best item and all other items, and show a lower bound of $Ω(K/Δ^2)$ indicating that our dependence on the main problem parameters $K$ and $Δ$ is tight (up to logarithmic factors).

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