Taposh Banerjee

Taposh Banerjee, Miao Liu, Jonathan P. How

Optimal control in non-stationary Markov decision processes (MDP) is a challenging problem. The aim in such a control problem is to maximize the long-term discounted reward when the transition dynamics or the reward function can change over time. When a prior knowledge of change statistics is available, the standard Bayesian approach to this problem is to reformulate it as a partially observable MDP (POMDP) and solve it using approximate POMDP solvers, which are typically computationally demanding. In this paper, the problem is analyzed through the viewpoint of quickest change detection (QCD), a set of tools for detecting a change in the distribution of a sequence of random variables. Current methods applying QCD to such problems only passively detect changes by following prescribed policies, without optimizing the choice of actions for long term performance. We demonstrate that ignoring the reward-detection trade-off can cause a significant loss in long term rewards, and propose a two threshold switching strategy to solve the issue. A non-Bayesian problem formulation is also proposed for scenarios where a Bayesian formulation cannot be defined. The performance of the proposed two threshold strategy is examined through numerical analysis on a non-stationary MDP task, and the strategy outperforms the state-of-the-art QCD methods in both Bayesian and non-Bayesian settings.

Suya Wu, Enmao Diao, Taposh Banerjee et al.

Classical quickest change detection algorithms require modeling pre-change and post-change distributions. Such an approach may not be feasible for various machine learning models because of the complexity of computing the explicit distributions. Additionally, these methods may suffer from a lack of robustness to model mismatch and noise. This paper develops a new variant of the classical Cumulative Sum (CUSUM) algorithm for the quickest change detection. This variant is based on Fisher divergence and the Hyvärinen score and is called the Score-based CUSUM (SCUSUM) algorithm. The SCUSUM algorithm allows the applications of change detection for unnormalized statistical models, i.e., models for which the probability density function contains an unknown normalization constant. The asymptotic optimality of the proposed algorithm is investigated by deriving expressions for average detection delay and the mean running time to a false alarm. Numerical results are provided to demonstrate the performance of the proposed algorithm.

Wuxia Chen, Taposh Banerjee, Jemin George et al.

The problem of reinforcement learning is considered where the environment or the model undergoes a change. An algorithm is proposed that an agent can apply in such a problem to achieve the optimal long-time discounted reward. The algorithm is model-free and learns the optimal policy by interacting with the environment. It is shown that the proposed algorithm has strong optimality properties. The effectiveness of the algorithm is also demonstrated using simulation results. The proposed algorithm exploits a fundamental reward-detection trade-off present in these problems and uses a quickest change detection algorithm to detect the model change. Recommendations are provided for faster detection of model changes and for smart initialization strategies.

Wuxia Chen, Taposh Banerjee, Vahid Tarokh

We address the problem of quickest change detection in Markov processes with unknown transition kernels. The key idea is to learn the conditional score $\nabla_{\mathbf{y}} \log p(\mathbf{y}|\mathbf{x})$ directly from sample pairs $( \mathbf{x},\mathbf{y})$, where both $\mathbf{x}$ and $\mathbf{y}$ are high-dimensional data generated by the same transition kernel. In this way, we avoid explicit likelihood evaluation and provide a practical way to learn the transition dynamics. Based on this estimation, we develop a score-based CUSUM procedure that uses conditional Hyvarinen score differences to detect changes in the kernel. To ensure bounded increments, we propose a truncated version of the statistic. With Hoeffding's inequality for uniformly ergodic Markov processes, we prove exponential lower bounds on the mean time to false alarm. We also prove asymptotic upper bounds on detection delay. These results give both theoretical guarantees and practical feasibility for score-based detection in high-dimensional Markov models.

Chao Huang, Wenshuo Zang, Carlo Pinciroli et al.

Compared with single robots, Multi-Robot Systems (MRS) can perform missions more efficiently due to the presence of multiple members with diverse capabilities. However, deploying an MRS in wide real-world environments is still challenging due to uncertain and various obstacles (e.g., building clusters and trees). With a limited understanding of environmental uncertainty on performance, an MRS cannot flexibly adjust its behaviors (e.g., teaming, load sharing, trajectory planning) to ensure both environment adaptation and task accomplishments. In this work, a novel joint preference landscape learning and behavior adjusting framework (PLBA) is designed. PLBA efficiently integrates real-time human guidance to MRS coordination and utilizes Sparse Variational Gaussian Processes with Varying Output Noise to quickly assess human preferences by leveraging spatial correlations between environment characteristics. An optimization-based behavior-adjusting method then safely adapts MRS behaviors to environments. To validate PLBA's effectiveness in MRS behavior adaption, a flood disaster search and rescue task was designed. 20 human users provided 1764 feedback based on human preferences obtained from MRS behaviors related to "task quality", "task progress", "robot safety". The prediction accuracy and adaptation speed results show the effectiveness of PLBA in preference learning and MRS behavior adaption.

Arman Adibi, Sanjeev Kulkarni, H. Vincent Poor et al.

This paper addresses the problem of detecting changes when only unnormalized pre- and post-change distributions are accessible. This situation happens in many scenarios in physics such as in ferromagnetism, crystallography, magneto-hydrodynamics, and thermodynamics, where the energy models are difficult to normalize. Our approach is based on the estimation of the Cumulative Sum (CUSUM) statistics, which is known to produce optimal performance. We first present an intuitively appealing approximation method. Unfortunately, this produces a biased estimator of the CUSUM statistics and may cause performance degradation. We then propose the Log-Partition Approximation Cumulative Sum (LPA-CUSUM) algorithm based on thermodynamic integration (TI) in order to estimate the log-ratio of normalizing constants of pre- and post-change distributions. It is proved that this approach gives an unbiased estimate of the log-partition function and the CUSUM statistics, and leads to an asymptotically optimal performance. Moreover, we derive a relationship between the required sample size for thermodynamic integration and the desired detection delay performance, offering guidelines for practical parameter selection. Numerical studies are provided demonstrating the efficacy of our approach.

Marko Angjelichinoski, John Choi, Taposh Banerjee et al.

Objective. We consider the cross-subject decoding problem from local field potential (LFP) signals, where training data collected from the prefrontal cortex (PFC) of a source subject is used to decode intended motor actions in a destination subject. Approach. We propose a novel supervised transfer learning technique, referred to as data centering, which is used to adapt the feature space of the source to the feature space of the destination. The key ingredients of data centering are the transfer functions used to model the deterministic component of the relationship between the source and destination feature spaces. We propose an efficient data-driven estimation approach for linear transfer functions that uses the first and second order moments of the class-conditional distributions. Main result. We apply our data centering technique with linear transfer functions for cross-subject decoding of eye movement intentions in an experiment where two macaque monkeys perform memory-guided visual saccades to one of eight target locations. The results show peak cross-subject decoding performance of $80\%$, which marks a substantial improvement over random choice decoder. In addition to this, data centering also outperforms standard sampling-based methods in setups with imbalanced training data. Significance. The analyses presented herein demonstrate that the proposed data centering is a viable novel technique for reliable LFP-based cross-subject brain-computer interfacing and neural prostheses.

Marko Angjelichinoski, Taposh Banerjee, John Choi et al.

We consider the problem of predicting eye movement goals from local field potentials (LFP) recorded through a multielectrode array in the macaque prefrontal cortex. The monkey is tasked with performing memory-guided saccades to one of eight targets during which LFP activity is recorded and used to train a decoder. Previous reports have mainly relied on the spectral amplitude of the LFPs as a feature in the decoding step to limited success, while neglecting the phase without proper theoretical justification. This paper formulates the problem of decoding eye movement intentions in a statistically optimal framework and uses Gaussian sequence modeling and Pinsker's theorem to generate minimax-optimal estimates of the LFP signals which are later used as features in the decoding step. The approach is shown to act as a low-pass filter and each LFP in the feature space is represented via its complex Fourier coefficients after appropriate shrinking such that higher frequency components are attenuated; this way, the phase information inherently present in the LFP signal is naturally embedded into the feature space. The proposed complex spectrum-based decoder achieves prediction accuracy of up to $94\%$ at superficial electrode depths near the surface of the prefrontal cortex, which marks a significant performance improvement over conventional power spectrum-based decoders.