Süleyman S. Kozat

Baturay Saglam, Furkan B. Mutlu, Dogan C. Cicek et al.

A widely-studied deep reinforcement learning (RL) technique known as Prioritized Experience Replay (PER) allows agents to learn from transitions sampled with non-uniform probability proportional to their temporal-difference (TD) error. Although it has been shown that PER is one of the most crucial components for the overall performance of deep RL methods in discrete action domains, many empirical studies indicate that it considerably underperforms actor-critic algorithms in continuous control. We theoretically show that actor networks cannot be effectively trained with transitions that have large TD errors. As a result, the approximate policy gradient computed under the Q-network diverges from the actual gradient computed under the optimal Q-function. Motivated by this, we introduce a novel experience replay sampling framework for actor-critic methods, which also regards issues with stability and recent findings behind the poor empirical performance of PER. The introduced algorithm suggests a new branch of improvements to PER and schedules effective and efficient training for both actor and critic networks. An extensive set of experiments verifies our theoretical claims and demonstrates that the introduced method significantly outperforms the competing approaches and obtains state-of-the-art results over the standard off-policy actor-critic algorithms.

Baturay Saglam, Doga Gurgunoglu, Suleyman S. Kozat

We introduce a novel deep reinforcement learning (DRL) approach to jointly optimize transmit beamforming and reconfigurable intelligent surface (RIS) phase shifts in a multiuser multiple input single output (MU-MISO) system to maximize the sum downlink rate under the phase-dependent reflection amplitude model. Our approach addresses the challenge of imperfect channel state information (CSI) and hardware impairments by considering a practical RIS amplitude model. We compare the performance of our approach against a vanilla DRL agent in two scenarios: perfect CSI and phase-dependent RIS amplitudes, and mismatched CSI and ideal RIS reflections. The results demonstrate that the proposed framework significantly outperforms the vanilla DRL agent under mismatch and approaches the golden standard. Our contributions include modifications to the DRL approach to address the joint design of transmit beamforming and phase shifts and the phase-dependent amplitude model. To the best of our knowledge, our method is the first DRL-based approach for the phase-dependent reflection amplitude model in RIS-aided MU-MISO systems. Our findings in this study highlight the potential of our approach as a promising solution to overcome hardware impairments in RIS-aided wireless communication systems.

Nargiz Kalantarova, Kyeongyeon Kim, Suleyman S. Kozat et al.

Formulations of the turbo equalization approach to iterative equalization and decoding vary greatly when channel knowledge is either partially or completely unknown. Maximum aposteriori probability (MAP) and minimum mean square error (MMSE) approaches leverage channel knowledge to make explicit use of soft information (priors over the transmitted data bits) in a manner that is distinctly nonlinear, appearing either in a trellis formulation (MAP) or inside an inverted matrix (MMSE). To date, nearly all adaptive turbo equalization methods either estimate the channel or use a direct adaptation equalizer in which estimates of the transmitted data are formed from an expressly linear function of the received data and soft information, with this latter formulation being most common. We study a class of direct adaptation turbo equalizers that are both adaptive and nonlinear functions of the soft information from the decoder. We introduce piecewise linear models based on context trees that can adaptively approximate the nonlinear dependence of the equalizer on the soft information such that it can choose both the partition regions as well as the locally linear equalizer coefficients in each region independently, with computational complexity that remains of the order of a traditional direct adaptive linear equalizer. This approach is guaranteed to asymptotically achieve the performance of the best piecewise linear equalizer and we quantify the MSE performance of the resulting algorithm and the convergence of its MSE to that of the linear minimum MSE estimator as the depth of the context tree and the data length increase.

Sait Tunc, Suleyman S. Kozat

We study optimal investment in a financial market having a finite number of assets from a signal processing perspective. We investigate how an investor should distribute capital over these assets and when he should reallocate the distribution of the funds over these assets to maximize the cumulative wealth over any investment period. In particular, we introduce a portfolio selection algorithm that maximizes the expected cumulative wealth in i.i.d. two-asset discrete-time markets where the market levies proportional transaction costs in buying and selling stocks. We achieve this using "threshold rebalanced portfolios", where trading occurs only if the portfolio breaches certain thresholds. Under the assumption that the relative price sequences have log-normal distribution from the Black-Scholes model, we evaluate the expected wealth under proportional transaction costs and find the threshold rebalanced portfolio that achieves the maximal expected cumulative wealth over any investment period. Our derivations can be readily extended to markets having more than two stocks, where these extensions are pointed out in the paper. As predicted from our derivations, we significantly improve the achieved wealth over portfolio selection algorithms from the literature on historical data sets.

Baturay Saglam, Suleyman S. Kozat

In continuous control, exploration is often performed through undirected strategies in which parameters of the networks or selected actions are perturbed by random noise. Although the deep setting of undirected exploration has been shown to improve the performance of on-policy methods, they introduce an excessive computational complexity and are known to fail in the off-policy setting. The intrinsically motivated exploration is an effective alternative to the undirected strategies, but they are usually studied for discrete action domains. In this paper, we investigate how intrinsic motivation can effectively be combined with deep reinforcement learning in the control of continuous systems to obtain a directed exploratory behavior. We adapt the existing theories on animal motivational systems into the reinforcement learning paradigm and introduce a novel and scalable directed exploration strategy. The introduced approach, motivated by the maximization of the value function's error, can benefit from a collected set of experiences by extracting useful information and unify the intrinsic exploration motivations in the literature under a single exploration objective. An extensive set of empirical studies demonstrate that our framework extends to larger and more diverse state spaces, dramatically improves the baselines, and outperforms the undirected strategies significantly.

Baturay Saglam, Dogan C. Cicek, Furkan B. Mutlu et al.

Compared to on-policy counterparts, off-policy model-free deep reinforcement learning can improve data efficiency by repeatedly using the previously gathered data. However, off-policy learning becomes challenging when the discrepancy between the underlying distributions of the agent's policy and collected data increases. Although the well-studied importance sampling and off-policy policy gradient techniques were proposed to compensate for this discrepancy, they usually require a collection of long trajectories and induce additional problems such as vanishing/exploding gradients or discarding many useful experiences, which eventually increases the computational complexity. Moreover, their generalization to either continuous action domains or policies approximated by deterministic deep neural networks is strictly limited. To overcome these limitations, we introduce a novel policy similarity measure to mitigate the effects of such discrepancy in continuous control. Our method offers an adequate single-step off-policy correction that is applicable to deterministic policy networks. Theoretical and empirical studies demonstrate that it can achieve a "safe" off-policy learning and substantially improve the state-of-the-art by attaining higher returns in fewer steps than the competing methods through an effective schedule of the learning rate in Q-learning and policy optimization.

Mustafa E. Aydın, Suleyman S. Kozat

We investigate nonlinear prediction in an online setting and introduce a hybrid model that effectively mitigates, via an end-to-end architecture, the need for hand-designed features and manual model selection issues of conventional nonlinear prediction/regression methods. In particular, we use recursive structures to extract features from sequential signals, while preserving the state information, i.e., the history, and boosted decision trees to produce the final output. The connection is in an end-to-end fashion and we jointly optimize the whole architecture using stochastic gradient descent, for which we also provide the backward pass update equations. In particular, we employ a recurrent neural network (LSTM) for adaptive feature extraction from sequential data and a gradient boosting machinery (soft GBDT) for effective supervised regression. Our framework is generic so that one can use other deep learning architectures for feature extraction (such as RNNs and GRUs) and machine learning algorithms for decision making as long as they are differentiable. We demonstrate the learning behavior of our algorithm on synthetic data and the significant performance improvements over the conventional methods over various real life datasets. Furthermore, we openly share the source code of the proposed method to facilitate further research.

Baturay Saglam, Dogan C. Cicek, Furkan B. Mutlu et al.

Learning in high dimensional continuous tasks is challenging, mainly when the experience replay memory is very limited. We introduce a simple yet effective experience sharing mechanism for deterministic policies in continuous action domains for the future off-policy deep reinforcement learning applications in which the allocated memory for the experience replay buffer is limited. To overcome the extrapolation error induced by learning from other agents' experiences, we facilitate our algorithm with a novel off-policy correction technique without any action probability estimates. We test the effectiveness of our method in challenging OpenAI Gym continuous control tasks and conclude that it can achieve a safe experience sharing across multiple agents and exhibits a robust performance when the replay memory is strictly limited.

Burak C. Civek, Suleyman S. Kozat

We investigate the problem of sequential linear data prediction for real life big data applications. The second order algorithms, i.e., Newton-Raphson Methods, asymptotically achieve the performance of the "best" possible linear data predictor much faster compared to the first order algorithms, e.g., Online Gradient Descent. However, implementation of these methods is not usually feasible in big data applications because of the extremely high computational needs. Regular implementation of the Newton-Raphson Methods requires a computational complexity in the order of $O(M^2)$ for an $M$ dimensional feature vector, while the first order algorithms need only $O(M)$. To this end, in order to eliminate this gap, we introduce a highly efficient implementation reducing the computational complexity of the Newton-Raphson Methods from quadratic to linear scale. The presented algorithm provides the well-known merits of the second order methods while offering the computational complexity of $O(M)$. We utilize the shifted nature of the consecutive feature vectors and do not rely on any statistical assumptions. Therefore, both regular and fast implementations achieve the same performance in the sense of mean square error. We demonstrate the computational efficiency of our algorithm on real life sequential big datasets. We also illustrate that the presented algorithm is numerically stable.

Arda Fazla, Mustafa Enes Aydin, Orhun Tamyigit et al.

We investigate ensemble methods for prediction in an online setting. Unlike all the literature in ensembling, for the first time, we introduce a new approach using a meta learner that effectively combines the base model predictions via using a superset of the features that is the union of the base models' feature vectors instead of the predictions themselves. Here, our model does not use the predictions of the base models as inputs to a machine learning algorithm, but choose the best possible combination at each time step based on the state of the problem. We explore three different constraint spaces for the ensembling of the base learners that linearly combines the base predictions, which are convex combinations where the components of the ensembling vector are all nonnegative and sum up to 1; affine combinations where the weight vector components are required to sum up to 1; and the unconstrained combinations where the components are free to take any real value. The constraints are both theoretically analyzed under known statistics and integrated into the learning procedure of the meta learner as a part of the optimization in an automated manner. To show the practical efficiency of the proposed method, we employ a gradient-boosted decision tree and a multi-layer perceptron separately as the meta learners. Our framework is generic so that one can use other machine learning architectures as the ensembler as long as they allow for a custom differentiable loss for minimization. We demonstrate the learning behavior of our algorithm on synthetic data and the significant performance improvements over the conventional methods over various real life datasets, extensively used in the well-known data competitions. Furthermore, we openly share the source code of the proposed method to facilitate further research and comparison.

Hakan Gokcesu, Suleyman S. Kozat

We study the prediction with expert advice setting, where the aim is to produce a decision by combining the decisions generated by a set of experts, e.g., independently running algorithms. We achieve the min-max optimal dynamic regret under the prediction with expert advice setting, i.e., we can compete against time-varying (not necessarily fixed) combinations of expert decisions in an optimal manner. Our end-algorithm is truly online with no prior information, such as the time horizon or loss ranges, which are commonly used by different algorithms in the literature. Both our regret guarantees and the min-max lower bounds are derived with the general consideration that the expert losses can have time-varying properties and are possibly unbounded. Our algorithm can be adapted for restrictive scenarios regarding both loss feedback and decision making. Our guarantees are universal, i.e., our end-algorithm can provide regret guarantee against any competitor sequence in a min-max optimal manner with logarithmic complexity. Note that, to our knowledge, for the prediction with expert advice problem, our algorithms are the first to produce such universally optimal, adaptive and truly online guarantees with no prior knowledge.

Nargiz Kalantarova, Mehmet A. Donmez, Suleyman S. Kozat

In this correspondence, we introduce a minimax regret criteria to the least squares problems with bounded data uncertainties and solve it using semi-definite programming. We investigate a robust minimax least squares approach that minimizes a worst case difference regret. The regret is defined as the difference between a squared data error and the smallest attainable squared data error of a least squares estimator. We then propose a robust regularized least squares approach to the regularized least squares problem under data uncertainties by using a similar framework. We show that both unstructured and structured robust least squares problems and robust regularized least squares problem can be put in certain semi-definite programming forms. Through several simulations, we demonstrate the merits of the proposed algorithms with respect to the the well-known alternatives in the literature.

Mehmet Efe Lorasdagi, Dogan Can Cicek, Furkan Burak Mutlu et al.

Background: Deep Deterministic Policy Gradient-based reinforcement learning algorithms utilize Actor-Critic architectures, where both networks are typically trained using identical batches of replayed transitions. However, the learning objectives and update dynamics of the Actor and Critic differ, raising concerns about whether uniform transition usage is optimal. Objectives: We aim to improve the performance of deep deterministic policy gradient algorithms by decoupling the transition batches used to train the Actor and the Critic. Our goal is to design an experience replay mechanism that provides appropriate learning signals to each component by using separate, tailored batches. Methods: We introduce Decoupled Prioritized Experience Replay (DPER), a novel approach that allows independent sampling of transition batches for the Actor and the Critic. DPER can be integrated into any off-policy deep reinforcement learning algorithm that operates in continuous control domains. We combine DPER with the state-of-the-art Twin Delayed DDPG algorithm and evaluate its performance across standard continuous control benchmarks. Results: DPER outperforms conventional experience replay strategies such as vanilla experience replay and prioritized experience replay in multiple MuJoCo tasks from the OpenAI Gym suite. Conclusions: Our findings show that decoupling experience replay for Actor and Critic networks can enhance training dynamics and final policy quality. DPER offers a generalizable mechanism that enhances performance for a wide class of actor-critic off-policy reinforcement learning algorithms.

Mustafa E. Aydın, Arda Fazla, Suleyman S. Kozat

We investigate nonlinear prediction/regression in an online setting and introduce a hybrid model that effectively mitigates, via a joint mechanism through a state space formulation, the need for domain-specific feature engineering issues of conventional nonlinear prediction models and achieves an efficient mix of nonlinear and linear components. In particular, we use recursive structures to extract features from raw sequential sequences and a traditional linear time series model to deal with the intricacies of the sequential data, e.g., seasonality, trends. The state-of-the-art ensemble or hybrid models typically train the base models in a disjoint manner, which is not only time consuming but also sub-optimal due to the separation of modeling or independent training. In contrast, as the first time in the literature, we jointly optimize an enhanced recurrent neural network (LSTM) for automatic feature extraction from raw data and an ARMA-family time series model (SARIMAX) for effectively addressing peculiarities associated with time series data. We achieve this by introducing novel state space representations for the base models, which are then combined to provide a full state space representation of the hybrid or the ensemble. Hence, we are able to jointly optimize both models in a single pass via particle filtering, for which we also provide the update equations. The introduced architecture is generic so that one can use other recurrent architectures, e.g., GRUs, traditional time series-specific models, e.g., ETS or other optimization methods, e.g., EKF, UKF. Due to such novel combination and joint optimization, we demonstrate significant improvements in widely publicized real life competition datasets. We also openly share our code for further research and replicability of our results.

Sait Tunc, Mehmet A. Donmez, Suleyman S. Kozat

We investigate how and when to diversify capital over assets, i.e., the portfolio selection problem, from a signal processing perspective. To this end, we first construct portfolios that achieve the optimal expected growth in i.i.d. discrete-time two-asset markets under proportional transaction costs. We then extend our analysis to cover markets having more than two stocks. The market is modeled by a sequence of price relative vectors with arbitrary discrete distributions, which can also be used to approximate a wide class of continuous distributions. To achieve the optimal growth, we use threshold portfolios, where we introduce a recursive update to calculate the expected wealth. We then demonstrate that under the threshold rebalancing framework, the achievable set of portfolios elegantly form an irreducible Markov chain under mild technical conditions. We evaluate the corresponding stationary distribution of this Markov chain, which provides a natural and efficient method to calculate the cumulative expected wealth. Subsequently, the corresponding parameters are optimized yielding the growth optimal portfolio under proportional transaction costs in i.i.d. discrete-time two-asset markets. As a widely known financial problem, we next solve optimal portfolio selection in discrete-time markets constructed by sampling continuous-time Brownian markets. For the case that the underlying discrete distributions of the price relative vectors are unknown, we provide a maximum likelihood estimator that is also incorporated in the optimization framework in our simulations.

Mehmet A. Donmez, Sait Tunc, Suleyman S. Kozat

We introduce a new analysis of an adaptive mixture method that combines outputs of two constituent filters running in parallel to model an unknown desired signal. This adaptive mixture is shown to achieve the mean square error (MSE) performance of the best constituent filter, and in some cases outperforms both, in the steady-state. However, the MSE analysis of this mixture in the steady-state and during the transient regions uses approximations and relies on statistical models on the underlying signals and systems. Hence, such an analysis may not be useful or valid for signals generated by various real life systems that show high degrees of nonstationarity, limit cycles and, in many cases, that are even chaotic. To this end, we perform the transient and the steady-state analysis of this adaptive mixture in a "strong" deterministic sense without any approximations in the derivations or statistical assumptions on the underlying signals such that our results are guaranteed to hold. In particular, we relate the time-accumulated squared estimation error of this adaptive mixture at any time to the time-accumulated squared estimation error of the optimal convex mixture of the constituent filters directly tuned to the underlying signal in an individual sequence manner.

Mehmet E. Lorasdagi, Mehmet Y. Turali, Suleyman S. Kozat

We investigate feature selection problem for generic machine learning models. We introduce a novel framework that selects features considering the outcomes of the model. Our framework introduces a novel feature masking approach to eliminate the features during the selection process, instead of completely removing them from the dataset. This allows us to use the same machine learning model during feature selection, unlike other feature selection methods where we need to train the machine learning model again as the dataset has different dimensions on each iteration. We obtain the mask operator using the predictions of the machine learning model, which offers a comprehensive view on the subsets of the features essential for the predictive performance of the model. A variety of approaches exist in the feature selection literature. However, to our knowledge, no study has introduced a training-free framework for a generic machine learning model to select features while considering the importance of the feature subsets as a whole, instead of focusing on the individual features. We demonstrate significant performance improvements on the real-life datasets under different settings using LightGBM and Multi-Layer Perceptron as our machine learning models. The high performance of our General Binary Mask Optimization algorithm stems from its feature masking approach to select features and its flexibility in the number of selected features. The algorithm selects features based on the validation performance of the machine learning model. Hence, the number of selected features is not predetermined and adjusts dynamically to the dataset. Additionally, we openly share the implementation or our code to encourage further research in this area.

Huseyin Karaca, Suleyman Serdar Kozat

We propose a soft gradient boosting framework for sequential regression that embeds a learnable linear feature transform within the boosting procedure. At each boosting iteration, we train a soft decision tree and learn a linear input feature transform Q together. This approach is particularly advantageous in high-dimensional, data-scarce scenarios, as it discovers the most relevant input representations while boosting. We demonstrate, using both synthetic and real-world datasets, that our method effectively and efficiently increases the performance by an end-to-end optimization of feature selection/transform and boosting while avoiding overfitting. We also extend our algorithm to differentiable non-linear transforms if overfitting is not a problem. To support reproducibility and future work, we share our code publicly.

Mehmet Y. Turali, Mehmet E. Lorasdagi, Ali T. Koc et al.

We study the problem of feature selection in general machine learning (ML) context, which is one of the most critical subjects in the field. Although, there exist many feature selection methods, however, these methods face challenges such as scalability, managing high-dimensional data, dealing with correlated features, adapting to variable feature importance, and integrating domain knowledge. To this end, we introduce the "Adaptive Feature Selection with Binary Masking" (AFS-BM) which remedies these problems. AFS-BM achieves this by joint optimization for simultaneous feature selection and model training. In particular, we do the joint optimization and binary masking to continuously adapt the set of features and model parameters during the training process. This approach leads to significant improvements in model accuracy and a reduction in computational requirements. We provide an extensive set of experiments where we compare AFS-BM with the established feature selection methods using well-known datasets from real-life competitions. Our results show that AFS-BM makes significant improvement in terms of accuracy and requires significantly less computational complexity. This is due to AFS-BM's ability to dynamically adjust to the changing importance of features during the training process, which an important contribution to the field. We openly share our code for the replicability of our results and to facilitate further research.

Selim F. Yilmaz, Suleyman S. Kozat

Streaming anomaly detection requires algorithms that operate under strict constraints: bounded memory, single-pass processing, and constant-time complexity. We present PySAD, a comprehensive Python framework addressing these challenges through a unified architecture. The framework implements 17+ streaming algorithms (LODA, Half-Space Trees, xStream) with specialized components including projectors, probability calibrators, and postprocessors. Unlike existing batch-focused frameworks, PySAD enables efficient real-time processing with bounded memory while maintaining compatibility with PyOD and scikit-learn. Supporting all learning paradigms for univariate and multivariate streams, PySAD provides the most comprehensive streaming anomaly detection toolkit in Python. The source code is publicly available at github.com/selimfirat/pysad.

Mehmet Efe Lorasdagi, Ahmet Berker Koc, Ali Taha Koc et al.

Traditional machine learning approaches assume that data comes from a single generating mechanism, which may not hold for most real life data. In these cases, the single mechanism assumption can result in suboptimal performance. We introduce a clustering framework that eliminates this assumption by grouping the data according to the relations between the features and the target values and we obtain multiple separate models to learn different parts of the data. We further extend our framework to applications having streaming data where we produce outcomes using an ensemble of models. For this, the ensemble weights are updated based on the incoming data batches. We demonstrate the performance of our approach over the widely-studied real life datasets, showing significant improvements over the traditional single-model approaches.

Arda Sarp Yenicesu, Furkan B. Mutlu, Suleyman S. Kozat et al.

The utilization of the experience replay mechanism enables agents to effectively leverage their experiences on several occasions. In previous studies, the sampling probability of the transitions was modified based on their relative significance. The process of reassigning sample probabilities for every transition in the replay buffer after each iteration is considered extremely inefficient. Hence, in order to enhance computing efficiency, experience replay prioritization algorithms reassess the importance of a transition as it is sampled. However, the relative importance of the transitions undergoes dynamic adjustments when the agent's policy and value function are iteratively updated. Furthermore, experience replay is a mechanism that retains the transitions generated by the agent's past policies, which could potentially diverge significantly from the agent's most recent policy. An increased deviation from the agent's most recent policy results in a greater frequency of off-policy updates, which has a negative impact on the agent's performance. In this paper, we develop a novel algorithm, Corrected Uniform Experience Replay (CUER), which stochastically samples the stored experience while considering the fairness among all other experiences without ignoring the dynamic nature of the transition importance by making sampled state distribution more on-policy. CUER provides promising improvements for off-policy continuous control algorithms in terms of sample efficiency, final performance, and stability of the policy during the training.

Selim Furkan Tekin, Suleyman Serdar Kozat

Existing approaches to the crime prediction problem are unsuccessful in expressing the details since they assign the probability values to large regions. This paper introduces a new architecture with the graph convolutional networks (GCN) and multivariate Gaussian distributions to perform high-resolution forecasting that applies to any spatiotemporal data. We tackle the sparsity problem in high resolution by leveraging the flexible structure of GCNs and providing a subdivision algorithm. We build our model with Graph Convolutional Gated Recurrent Units (Graph-ConvGRU) to learn spatial, temporal, and categorical relations. In each node of the graph, we learn a multivariate probability distribution from the extracted features of GCNs. We perform experiments on real-life and synthetic datasets, and our model obtains the best validation and the best test score among the baseline models with significant improvements. We show that our model is not only generative but also precise.

Dogan C. Cicek, Enes Duran, Baturay Saglam et al.

Value-based deep Reinforcement Learning (RL) algorithms suffer from the estimation bias primarily caused by function approximation and temporal difference (TD) learning. This problem induces faulty state-action value estimates and therefore harms the performance and robustness of the learning algorithms. Although several techniques were proposed to tackle, learning algorithms still suffer from this bias. Here, we introduce a technique that eliminates the estimation bias in off-policy continuous control algorithms using the experience replay mechanism. We adaptively learn the weighting hyper-parameter beta in the Weighted Twin Delayed Deep Deterministic Policy Gradient algorithm. Our method is named Adaptive-WD3 (AWD3). We show through continuous control environments of OpenAI gym that our algorithm matches or outperforms the state-of-the-art off-policy policy gradient learning algorithms.

Dogan C. Cicek, Enes Duran, Baturay Saglam et al.

The experience replay mechanism allows agents to use the experiences multiple times. In prior works, the sampling probability of the transitions was adjusted according to their importance. Reassigning sampling probabilities for every transition in the replay buffer after each iteration is highly inefficient. Therefore, experience replay prioritization algorithms recalculate the significance of a transition when the corresponding transition is sampled to gain computational efficiency. However, the importance level of the transitions changes dynamically as the policy and the value function of the agent are updated. In addition, experience replay stores the transitions are generated by the previous policies of the agent that may significantly deviate from the most recent policy of the agent. Higher deviation from the most recent policy of the agent leads to more off-policy updates, which is detrimental for the agent. In this paper, we develop a novel algorithm, Batch Prioritizing Experience Replay via KL Divergence (KLPER), which prioritizes batch of transitions rather than directly prioritizing each transition. Moreover, to reduce the off-policyness of the updates, our algorithm selects one batch among a certain number of batches and forces the agent to learn through the batch that is most likely generated by the most recent policy of the agent. We combine our algorithm with Deep Deterministic Policy Gradient and Twin Delayed Deep Deterministic Policy Gradient and evaluate it on various continuous control tasks. KLPER provides promising improvements for deep deterministic continuous control algorithms in terms of sample efficiency, final performance, and stability of the policy during the training.

Baturay Saglam, Furkan Burak Mutlu, Dogan Can Cicek et al.

Approximation of the value functions in value-based deep reinforcement learning induces overestimation bias, resulting in suboptimal policies. We show that when the reinforcement signals received by the agents have a high variance, deep actor-critic approaches that overcome the overestimation bias lead to a substantial underestimation bias. We first address the detrimental issues in the existing approaches that aim to overcome such underestimation error. Then, through extensive statistical analysis, we introduce a novel, parameter-free Deep Q-learning variant to reduce this underestimation bias in deterministic policy gradients. By sampling the weights of a linear combination of two approximate critics from a highly shrunk estimation bias interval, our Q-value update rule is not affected by the variance of the rewards received by the agents throughout learning. We test the performance of the introduced improvement on a set of MuJoCo and Box2D continuous control tasks and demonstrate that it considerably outperforms the existing approaches and improves the state-of-the-art by a significant margin.

Baturay Saglam, Enes Duran, Dogan C. Cicek et al.

In value-based deep reinforcement learning methods, approximation of value functions induces overestimation bias and leads to suboptimal policies. We show that in deep actor-critic methods that aim to overcome the overestimation bias, if the reinforcement signals received by the agent have a high variance, a significant underestimation bias arises. To minimize the underestimation, we introduce a parameter-free, novel deep Q-learning variant. Our Q-value update rule combines the notions behind Clipped Double Q-learning and Maxmin Q-learning by computing the critic objective through the nested combination of maximum and minimum operators to bound the approximate value estimates. We evaluate our modification on the suite of several OpenAI Gym continuous control tasks, improving the state-of-the-art in every environment tested.

Selim Furkan Tekin, Arda Fazla, Suleyman Serdar Kozat

Numerical weather forecasting using high-resolution physical models often requires extensive computational resources on supercomputers, which diminishes their wide usage in most real-life applications. As a remedy, applying deep learning methods has revealed innovative solutions within this field. To this end, we introduce a novel deep learning architecture for forecasting high-resolution spatio-temporal weather data. Our approach extends the conventional encoder-decoder structure by integrating Convolutional Long-short Term Memory and Convolutional Neural Networks. In addition, we incorporate attention and context matcher mechanisms into the model architecture. Our Weather Model achieves significant performance improvements compared to baseline deep learning models, including ConvLSTM, TrajGRU, and U-Net. Our experimental evaluation involves high-scale, real-world benchmark numerical weather datasets, namely the ERA5 hourly dataset on pressure levels and WeatherBench. Our results demonstrate substantial improvements in identifying spatial and temporal correlations with attention matrices focusing on distinct parts of the input series to model atmospheric circulations. We also compare our model with high-resolution physical models using the benchmark metrics and show that our Weather Model is accurate and easy to interpret.

Selim F. Yilmaz, E. Batuhan Kaynak, Aykut Koç et al.

We investigate cross-lingual sentiment analysis, which has attracted significant attention due to its applications in various areas including market research, politics and social sciences. In particular, we introduce a sentiment analysis framework in multi-label setting as it obeys Plutchik wheel of emotions. We introduce a novel dynamic weighting method that balances the contribution from each class during training, unlike previous static weighting methods that assign non-changing weights based on their class frequency. Moreover, we adapt the focal loss that favors harder instances from single-label object recognition literature to our multi-label setting. Furthermore, we derive a method to choose optimal class-specific thresholds that maximize the macro-f1 score in linear time complexity. Through an extensive set of experiments, we show that our method obtains the state-of-the-art performance in 7 of 9 metrics in 3 different languages using a single model compared to the common baselines and the best-performing methods in the SemEval competition. We publicly share our code for our model, which can perform sentiment analysis in 100 languages, to facilitate further research.

Oguzhan Karaahmetoglu, Suleyman S. Kozat

We study the spatio-temporal prediction problem and introduce a novel point-process-based prediction algorithm. Spatio-temporal prediction is extensively studied in Machine Learning literature due to its critical real-life applications such as crime, earthquake, and social event prediction. Despite these thorough studies, specific problems inherent to the application domain are not yet fully explored. Here, we address the non-stationary spatio-temporal prediction problem on both densely and sparsely distributed sequences. We introduce a probabilistic approach that partitions the spatial domain into subregions and models the event arrivals in each region with interacting point-processes. Our algorithm can jointly learn the spatial partitioning and the interaction between these regions through a gradient-based optimization procedure. Finally, we demonstrate the performance of our algorithm on both simulated data and two real-life datasets. We compare our approach with baseline and state-of-the-art deep learning-based approaches, where we achieve significant performance improvements. Moreover, we also show the effect of using different parameters on the overall performance through empirical results and explain the procedure for choosing the parameters.

Fatih Ilhan, Oguzhan Karaahmetoglu, Ismail Balaban et al.

We investigate nonlinear regression for nonstationary sequential data. In most real-life applications such as business domains including finance, retail, energy and economy, timeseries data exhibits nonstationarity due to the temporally varying dynamics of the underlying system. We introduce a novel recurrent neural network (RNN) architecture, which adaptively switches between internal regimes in a Markovian way to model the nonstationary nature of the given data. Our model, Markovian RNN employs a hidden Markov model (HMM) for regime transitions, where each regime controls hidden state transitions of the recurrent cell independently. We jointly optimize the whole network in an end-to-end fashion. We demonstrate the significant performance gains compared to vanilla RNN and conventional methods such as Markov Switching ARIMA through an extensive set of experiments with synthetic and real-life datasets. We also interpret the inferred parameters and regime belief values to analyze the underlying dynamics of the given sequences.

Oguzhan Karaahmetoglu, Fatih Ilhan, Ismail Balaban et al.

We study anomaly detection and introduce an algorithm that processes variable length, irregularly sampled sequences or sequences with missing values. Our algorithm is fully unsupervised, however, can be readily extended to supervised or semisupervised cases when the anomaly labels are present as remarked throughout the paper. Our approach uses the Long Short Term Memory (LSTM) networks in order to extract temporal features and find the most relevant feature vectors for anomaly detection. We incorporate the sampling time information to our model by modulating the standard LSTM model with time modulation gates. After obtaining the most relevant features from the LSTM, we label the sequences using a Support Vector Data Descriptor (SVDD) model. We introduce a loss function and then jointly optimize the feature extraction and sequence processing mechanisms in an end-to-end manner. Through this joint optimization, the LSTM extracts the most relevant features for anomaly detection later to be used in the SVDD, hence completely removes the need for feature selection by expert knowledge. Furthermore, we provide a training algorithm for the online setup, where we optimize our model parameters with individual sequences as the new data arrives. Finally, on real-life datasets, we show that our model significantly outperforms the standard approaches thanks to its combination of LSTM with SVDD and joint optimization.

S. Onur Sahin, Suleyman S. Kozat

We investigate regression for variable length sequential data containing missing samples and introduce a novel tree architecture based on the Long Short-Term Memory (LSTM) networks. In our architecture, we employ a variable number of LSTM networks, which use only the existing inputs in the sequence, in a tree-like architecture without any statistical assumptions or imputations on the missing data, unlike all the previous approaches. In particular, we incorporate the missingness information by selecting a subset of these LSTM networks based on "presence-pattern" of a certain number of previous inputs. From the mixture of experts perspective, we train different LSTM networks as our experts for various missingness patterns and then combine their outputs to generate the final prediction. We also provide the computational complexity analysis of the proposed architecture, which is in the same order of the complexity of the conventional LSTM architectures for the sequence length. Our method can be readily extended to similar structures such as GRUs, RNNs as remarked in the paper. In the experiments, we achieve significant performance improvements with respect to the state-of-the-art methods for the well-known financial and real life datasets.

N. Mert Vural, Fatih Ilhan, Selim F. Yilmaz et al.

Recurrent Neural Networks (RNNs) are widely used for online regression due to their ability to generalize nonlinear temporal dependencies. As an RNN model, Long-Short-Term-Memory Networks (LSTMs) are commonly preferred in practice, as these networks are capable of learning long-term dependencies while avoiding the vanishing gradient problem. However, due to their large number of parameters, training LSTMs requires considerably longer training time compared to simple RNNs (SRNNs). In this paper, we achieve the online regression performance of LSTMs with SRNNs efficiently. To this end, we introduce a first-order training algorithm with a linear time complexity in the number of parameters. We show that when SRNNs are trained with our algorithm, they provide very similar regression performance with the LSTMs in two to three times shorter training time. We provide strong theoretical analysis to support our experimental results by providing regret bounds on the convergence rate of our algorithm. Through an extensive set of experiments, we verify our theoretical work and demonstrate significant performance improvements of our algorithm with respect to LSTMs and the other state-of-the-art learning models.

Selim F. Yilmaz, Suleyman S. Kozat

We investigate unsupervised anomaly detection for high-dimensional data and introduce a deep metric learning (DML) based framework. In particular, we learn a distance metric through a deep neural network. Through this metric, we project the data into the metric space that better separates the anomalies from the normal data and reduces the effect of the curse of dimensionality for high-dimensional data. We present a novel data distillation method through self-supervision to remedy the conventional practice of assuming all data as normal. We also employ the hard mining technique from the DML literature. We show these components improve the performance of our model and significantly reduce the running time. Through an extensive set of experiments on the 14 real-world datasets, our method demonstrates significant performance gains compared to the state-of-the-art unsupervised anomaly detection methods, e.g., an absolute improvement between 4.44% and 11.74% on the average over the 14 datasets. Furthermore, we share the source code of our method on Github to facilitate further research.

Fatih Ilhan, Suleyman Serdar Kozat

We investigate spatio-temporal event analysis using point processes. Inferring the dynamics of event sequences spatiotemporally has many practical applications including crime prediction, social media analysis, and traffic forecasting. In particular, we focus on spatio-temporal Hawkes processes that are commonly used due to their capability to capture excitations between event occurrences. We introduce a novel inference framework based on randomized transformations and gradient descent to learn the process. We replace the spatial kernel calculations by randomized Fourier feature-based transformations. The introduced randomization by this representation provides flexibility while modeling the spatial excitation between events. Moreover, the system described by the process is expressed within closed-form in terms of scalable matrix operations. During the optimization, we use maximum likelihood estimation approach and gradient descent while properly handling positivity and orthonormality constraints. The experiment results show the improvements achieved by the introduced method in terms of fitting capability in synthetic and real datasets with respect to the conventional inference methods in the spatio-temporal Hawkes process literature. We also analyze the triggering interactions between event types and how their dynamics change in space and time through the interpretation of learned parameters.

Oguzhan Karaahmetoglu, Suleyman Serdar Kozat

We study the spatio-temporal prediction problem, which has attracted the attention of many researchers due to its critical real-life applications. In particular, we introduce a novel approach to this problem. Our approach is based on the Hawkes process, which is a non-stationary and self-exciting point process. We extend the formulations of a standard point process model that can represent time-series data to represent a spatio-temporal data. We model the data as nonstationary in time and space. Furthermore, we partition the spatial region we are working on into subregions via an adaptive decision tree and model the source statistics in each subregion with individual but mutually interacting point processes. We also provide a gradient based joint optimization algorithm for the point process and decision tree parameters. Thus, we introduce a model that can jointly infer the source statistics and an adaptive partitioning of the spatial region. Finally, we provide experimental results on real-life data, which provides significant improvement due to space adaptation and joint optimization compared to standard well-known methods in the literature.

N. Mert Vural, Selim F. Yilmaz, Fatih Ilhan et al.

We investigate online nonlinear regression with continually running recurrent neural network networks (RNNs), i.e., RNN-based online learning. For RNN-based online learning, we introduce an efficient first-order training algorithm that theoretically guarantees to converge to the optimum network parameters. Our algorithm is truly online such that it does not make any assumption on the learning environment to guarantee convergence. Through numerical simulations, we verify our theoretical results and illustrate significant performance improvements achieved by our algorithm with respect to the state-of-the-art RNN training methods.

Nuri Mert Vural, Fatih Ilhan, Suleyman S. Kozat

We investigate the convergence and stability properties of the decoupled extended Kalman filter learning algorithm (DEKF) within the long-short term memory network (LSTM) based online learning framework. For this purpose, we model DEKF as a perturbed extended Kalman filter and derive sufficient conditions for its stability during LSTM training. We show that if the perturbations -- introduced due to decoupling -- stay bounded, DEKF learns LSTM parameters with similar convergence and stability properties of the global extended Kalman filter learning algorithm. We verify our results with several numerical simulations and compare DEKF with other LSTM training methods. In our simulations, we also observe that the well-known hyper-parameter selection approaches used for DEKF in the literature satisfy our conditions.

N. Mert Vural, Hakan Gokcesu, Kaan Gokcesu et al.

We investigate the adversarial bandit problem with multiple plays under semi-bandit feedback. We introduce a highly efficient algorithm that asymptotically achieves the performance of the best switching $m$-arm strategy with minimax optimal regret bounds. To construct our algorithm, we introduce a new expert advice algorithm for the multiple-play setting. By using our expert advice algorithm, we additionally improve the best-known high-probability bound for the multi-play setting by $O(\sqrt{m})$. Our results are guaranteed to hold in an individual sequence manner since we have no statistical assumption on the bandit arm gains. Through an extensive set of experiments involving synthetic and real data, we demonstrate significant performance gains achieved by the proposed algorithm with respect to the state-of-the-art algorithms.

N. Mert Vural, Salih Ergüt, Suleyman S. Kozat

We study adaptive (or online) nonlinear regression with Long-Short-Term-Memory (LSTM) based networks, i.e., LSTM-based adaptive learning. In this context, we introduce an efficient Extended Kalman filter (EKF) based second-order training algorithm. Our algorithm is truly online, i.e., it does not assume any underlying data generating process and future information, except that the target sequence is bounded. Through an extensive set of experiments, we demonstrate significant performance gains achieved by our algorithm with respect to the state-of-the-art methods. Here, we mainly show that our algorithm consistently provides 10 to 45\% improvement in the accuracy compared to the widely-used adaptive methods Adam, RMSprop, and DEKF, and comparable performance to EKF with a 10 to 15 times reduction in the run-time.

Hakan Gokcesu, Suleyman S. Kozat

We introduce an online convex optimization algorithm which utilizes projected subgradient descent with optimal adaptive learning rates. Our method provides second-order minimax-optimal dynamic regret guarantee (i.e. dependent on the sum of squared subgradient norms) for a sequence of general convex functions, which may not have strong convexity, smoothness, exp-concavity or even Lipschitz-continuity. The regret guarantee is against any comparator decision sequence with bounded path variation (i.e. sum of the distances between successive decisions). We generate the lower bound of the worst-case second-order dynamic regret by incorporating actual subgradient norms. We show that this lower bound matches with our regret guarantee within a constant factor, which makes our algorithm minimax optimal. We also derive the extension for learning in each decision coordinate individually. We demonstrate how to best preserve our regret guarantee in a truly online manner, when the bound on path variation of the comparator sequence grows in time or the feedback regarding such bound arrives partially as time goes on. We further build on our algorithm to eliminate the need of any knowledge on the comparator path variation, and provide minimax optimal second-order regret guarantees with no a priori information. Our approach can compete against all comparator sequences simultaneously (universally) in a minimax optimal manner, i.e. each regret guarantee depends on the respective comparator path variation. We discuss modifications to our approach which address complexity reductions for time, computation and memory. We further improve our results by making the regret guarantees also dependent on comparator sets' diameters in addition to the respective path variations.

Hakan Gokcesu, Kaan Gokcesu, Suleyman Serdar Kozat

We study the min-max optimization problem where each function contributing to the max operation is strongly-convex and smooth with bounded gradient in the search domain. By smoothing the max operator, we show the ability to achieve an arbitrarily small positive optimality gap of $δ$ in $\tilde{O}(1/\sqrtδ)$ computational complexity (up to logarithmic factors) as opposed to the state-of-the-art strong-convexity computational requirement of $O(1/δ)$. We apply this important result to the well-known minimal bounding sphere problem and demonstrate that we can achieve a $(1+\varepsilon)$-approximation of the minimal bounding sphere, i.e. identify an hypersphere enclosing a total of $n$ given points in the $d$ dimensional unbounded space $\mathbb{R}^d$ with a radius at most $(1+\varepsilon)$ times the actual minimal bounding sphere radius for an arbitrarily small positive $\varepsilon$, in $\tilde{O}(n d /\sqrt{\varepsilon})$ computational time as opposed to the state-of-the-art approach of core-set methodology, which needs $O(n d /\varepsilon)$ computational time.

Hakan Gokcesu, Suleyman S. Kozat

We study online convex optimization under stochastic sub-gradient observation faults, where we introduce adaptive algorithms with minimax optimal regret guarantees. We specifically study scenarios where our sub-gradient observations can be noisy or even completely missing in a stochastic manner. To this end, we propose algorithms based on sub-gradient descent method, which achieve tight minimax optimal regret bounds. When necessary, these algorithms utilize properties of the underlying stochastic settings to optimize their learning rates (step sizes). These optimizations are the main factor in providing the minimax optimal performance guarantees, especially when observations are stochastically missing. However, in real world scenarios, these properties of the underlying stochastic settings may not be revealed to the optimizer. For such a scenario, we propose a blind algorithm that estimates these properties empirically in a generally applicable manner. Through extensive experiments, we show that this empirical approach is a natural combination of regular stochastic gradient descent and the minimax optimal algorithms (which work best for randomized and adversarial function sequences, respectively).

Mohammadreza Mohaghegh Neyshabouri, Suleyman Serdar Kozat

We introduce an online outlier detection algorithm to detect outliers in a sequentially observed data stream. For this purpose, we use a two-stage filtering and hedging approach. In the first stage, we construct a multi-modal probability density function to model the normal samples. In the second stage, given a new observation, we label it as an anomaly if the value of aforementioned density function is below a specified threshold at the newly observed point. In order to construct our multi-modal density function, we use an incremental decision tree to construct a set of subspaces of the observation space. We train a single component density function of the exponential family using the observations, which fall inside each subspace represented on the tree. These single component density functions are then adaptively combined to produce our multi-modal density function, which is shown to achieve the performance of the best convex combination of the density functions defined on the subspaces. As we observe more samples, our tree grows and produces more subspaces. As a result, our modeling power increases in time, while mitigating overfitting issues. In order to choose our threshold level to label the observations, we use an adaptive thresholding scheme. We show that our adaptive threshold level achieves the performance of the optimal pre-fixed threshold level, which knows the observation labels in hindsight. Our algorithm provides significant performance improvements over the state of the art in our wide set of experiments involving both synthetic as well as real data.

Tolga Ergen, Ali Hassan Mirza, Suleyman Serdar Kozat

We investigate anomaly detection in an unsupervised framework and introduce Long Short Term Memory (LSTM) neural network based algorithms. In particular, given variable length data sequences, we first pass these sequences through our LSTM based structure and obtain fixed length sequences. We then find a decision function for our anomaly detectors based on the One Class Support Vector Machines (OC-SVM) and Support Vector Data Description (SVDD) algorithms. As the first time in the literature, we jointly train and optimize the parameters of the LSTM architecture and the OC-SVM (or SVDD) algorithm using highly effective gradient and quadratic programming based training methods. To apply the gradient based training method, we modify the original objective criteria of the OC-SVM and SVDD algorithms, where we prove the convergence of the modified objective criteria to the original criteria. We also provide extensions of our unsupervised formulation to the semi-supervised and fully supervised frameworks. Thus, we obtain anomaly detection algorithms that can process variable length data sequences while providing high performance, especially for time series data. Our approach is generic so that we also apply this approach to the Gated Recurrent Unit (GRU) architecture by directly replacing our LSTM based structure with the GRU based structure. In our experiments, we illustrate significant performance gains achieved by our algorithms with respect to the conventional methods.

Burak C. Civek, Ibrahim Delibalta, Suleyman S. Kozat

We introduce highly efficient online nonlinear regression algorithms that are suitable for real life applications. We process the data in a truly online manner such that no storage is needed, i.e., the data is discarded after being used. For nonlinear modeling we use a hierarchical piecewise linear approach based on the notion of decision trees where the space of the regressor vectors is adaptively partitioned based on the performance. As the first time in the literature, we learn both the piecewise linear partitioning of the regressor space as well as the linear models in each region using highly effective second order methods, i.e., Newton-Raphson Methods. Hence, we avoid the well known over fitting issues by using piecewise linear models, however, since both the region boundaries as well as the linear models in each region are trained using the second order methods, we achieve substantial performance compared to the state of the art. We demonstrate our gains over the well known benchmark data sets and provide performance results in an individual sequence manner guaranteed to hold without any statistical assumptions. Hence, the introduced algorithms address computational complexity issues widely encountered in real life applications while providing superior guaranteed performance in a strong deterministic sense.

Mohammadreza Mohaghegh Neyshabouri, Kaan Gokcesu, Huseyin Ozkan et al.

We propose online algorithms for sequential learning in the contextual multi-armed bandit setting. Our approach is to partition the context space and then optimally combine all of the possible mappings between the partition regions and the set of bandit arms in a data driven manner. We show that in our approach, the best mapping is able to approximate the best arm selection policy to any desired degree under mild Lipschitz conditions. Therefore, we design our algorithms based on the optimal adaptive combination and asymptotically achieve the performance of the best mapping as well as the best arm selection policy. This optimality is also guaranteed to hold even in adversarial environments since we do not rely on any statistical assumptions regarding the contexts or the loss of the bandit arms. Moreover, we design efficient implementations for our algorithms in various hierarchical partitioning structures such as lexicographical or arbitrary position splitting and binary trees (and several other partitioning examples). For instance, in the case of binary tree partitioning, the computational complexity is only log-linear in the number of regions in the finest partition. In conclusion, we provide significant performance improvements by introducing upper bounds (w.r.t. the best arm selection policy) that are mathematically proven to vanish in the average loss per round sense at a faster rate compared to the state-of-the-art. Our experimental work extensively covers various scenarios ranging from bandit settings to multi-class classification with real and synthetic data. In these experiments, we show that our algorithms are highly superior over the state-of-the-art techniques while maintaining the introduced mathematical guarantees and a computationally decent scalability.

Muhammed O. Sayin, Suleyman S. Kozat, Tamer Başar

We construct team-optimal estimation algorithms over distributed networks for state estimation in the finite-horizon mean-square error (MSE) sense. Here, we have a distributed collection of agents with processing and cooperation capabilities. These agents observe noisy samples of a desired state through a linear model and seek to learn this state by interacting with each other. Although this problem has attracted significant attention and been studied extensively in fields including machine learning and signal processing, all the well-known strategies do not achieve team-optimal learning performance in the finite-horizon MSE sense. To this end, we formulate the finite-horizon distributed minimum MSE (MMSE) when there is no restriction on the size of the disclosed information, i.e., oracle performance, over an arbitrary network topology. Subsequently, we show that exchange of local estimates is sufficient to achieve the oracle performance only over certain network topologies. By inspecting these network structures, we propose recursive algorithms achieving the oracle performance through the disclosure of local estimates. For practical implementations we also provide approaches to reduce the complexity of the algorithms through the time-windowing of the observations. Finally, in the numerical examples, we demonstrate the superior performance of the introduced algorithms in the finite-horizon MSE sense due to optimal estimation.

Dariush Kari, Nuri Denizcan Vanli, Suleyman Serdar Kozat

We investigate underwater acoustic (UWA) channel equalization and introduce hierarchical and adaptive nonlinear channel equalization algorithms that are highly efficient and provide significantly improved bit error rate (BER) performance. Due to the high complexity of nonlinear equalizers and poor performance of linear ones, to equalize highly difficult underwater acoustic channels, we employ piecewise linear equalizers. However, in order to achieve the performance of the best piecewise linear model, we use a tree structure to hierarchically partition the space of the received signal. Furthermore, the equalization algorithm should be completely adaptive, since due to the highly non-stationary nature of the underwater medium, the optimal MSE equalizer as well as the best piecewise linear equalizer changes in time. To this end, we introduce an adaptive piecewise linear equalization algorithm that not only adapts the linear equalizer at each region but also learns the complete hierarchical structure with a computational complexity only polynomial in the number of nodes of the tree. Furthermore, our algorithm is constructed to directly minimize the final squared error without introducing any ad-hoc parameters. We demonstrate the performance of our algorithms through highly realistic experiments performed on accurately simulated underwater acoustic channels.