Algorithmic collusion has emerged as a central question in AI: Will the interaction between different AI agents deployed in markets lead to collusion? More generally, understanding how emergent behavior, be it a cartel or market dominance from more advanced bots, affects the market overall is an important research question. We propose a hierarchical multi-agent reinforcement learning framework to study algorithmic collusion in market making. The framework includes a self-interested market maker (Agent~A), which is trained in an uncertain environment shaped by an adversary, and three bottom-layer competitors: the self-interested Agent~B1 (whose objective is to maximize its own PnL), the competitive Agent~B2 (whose objective is to minimize the PnL of its opponent), and the hybrid Agent~B$^\star$, which can modulate between the behavior of the other two. To analyze how these agents shape the behavior of each other and affect market outcomes, we propose interaction-level metrics that quantify behavioral asymmetry and system-level dynamics, while providing signals potentially indicative of emergent interaction patterns. Experimental results show that Agent~B2 secures dominant performance in a zero-sum setting against B1, aggressively capturing order flow while tightening average spreads, thus improving market execution efficiency. In contrast, Agent~B$^\star$ exhibits a self-interested inclination when co-existing with other profit-seeking agents, securing dominant market share through adaptive quoting, yet exerting a milder adverse impact on the rewards of Agents~A and B1 compared to B2. These findings suggest that adaptive incentive control supports more sustainable strategic co-existence in heterogeneous agent environments and offers a structured lens for evaluating behavioral design in algorithmic trading systems.

This study evaluates the performance of 41 machine learning models, including 21 classifiers and 20 regressors, in predicting Bitcoin prices for algorithmic trading. By examining these models under various market conditions, we highlight their accuracy, robustness, and adaptability to the volatile cryptocurrency market. Our comprehensive analysis reveals the strengths and limitations of each model, providing critical insights for developing effective trading strategies. We employ both machine learning metrics (e.g., Mean Absolute Error, Root Mean Squared Error) and trading metrics (e.g., Profit and Loss percentage, Sharpe Ratio) to assess model performance. Our evaluation includes backtesting on historical data, forward testing on recent unseen data, and real-world trading scenarios, ensuring the robustness and practical applicability of our models. Key findings demonstrate that certain models, such as Random Forest and Stochastic Gradient Descent, outperform others in terms of profit and risk management. These insights offer valuable guidance for traders and researchers aiming to leverage machine learning for cryptocurrency trading.

This study presents an unsupervised machine learning approach for optimizing Profit and Loss (PnL) in quantitative finance. Our algorithm, akin to an unsupervised variant of linear regression, maximizes the Sharpe Ratio of PnL generated from signals constructed linearly from exogenous variables. The methodology employs a linear relationship between exogenous variables and the trading signal, with the objective of maximizing the Sharpe Ratio through parameter optimization. Empirical application on an ETF representing U.S. Treasury bonds demonstrates the model's effectiveness, supported by regularization techniques to mitigate overfitting. The study concludes with potential avenues for further development, including generalized time steps and enhanced corrective terms.

Decentralized exchanges (DEXs) are a cornerstone of decentralized finance (DeFi), allowing users to trade cryptocurrencies without the need for third-party authorization. Investors are incentivized to deposit assets into liquidity pools, against which users can trade directly, while paying fees to liquidity providers (LPs). However, a number of unresolved issues related to capital efficiency and market risk hinder DeFi's further development. Uniswap V3, a leading and groundbreaking DEX project, addresses capital efficiency by enabling LPs to concentrate their liquidity within specific price ranges for deposited assets. Nevertheless, this approach exacerbates market risk, as LPs earn trading fees only when asset prices are within these predetermined brackets. To mitigate this issue, this paper introduces a deep reinforcement learning (DRL) solution designed to adaptively adjust these price ranges, maximizing profits and mitigating market risks. Our approach also neutralizes price-change risks by hedging the liquidity position through a rebalancing portfolio in a centralized futures exchange. The DRL policy aims to optimize trading fees earned by LPs against associated costs, such as gas fees and hedging expenses, which is referred to as loss-versus-rebalancing (LVR). Using simulations with a profit-and-loss (PnL) benchmark, our method demonstrates superior performance in ETH/USDC and ETH/USDT pools compared to existing baselines. We believe that this strategy not only offers investors a valuable asset management tool but also introduces a new incentive mechanism for DEX designers.

Pairs trading is a family of trading techniques that determine their policies based on monitoring the relationships between pairs of assets. A common pairs trading approach relies on describing the pair-wise relationship as a linear Space State (SS) model with Gaussian noise. This representation facilitates extracting financial indicators with low complexity and latency using a Kalman Filter (KF), that are then processed using classic policies such as Bollinger Bands (BB). However, such SS models are inherently approximated and mismatched, often degrading the revenue. In this work, we propose KalmenNet-aided Bollinger bands Pairs Trading (KBPT), a deep learning aided policy that augments the operation of KF-aided BB trading. KBPT is designed by formulating an extended SS model for pairs trading that approximates their relationship as holding partial co-integration. This SS model is utilized by a trading policy that augments KF-BB trading with a dedicated neural network based on the KalmanNet architecture. The resulting KBPT is trained in a two-stage manner which first tunes the tracking algorithm in an unsupervised manner independently of the trading task, followed by its adaptation to track the financial indicators to maximize revenue while approximating BB with a differentiable mapping. KBPT thus leverages data to overcome the approximated nature of the SS model, converting the KF-BB policy into a trainable model. We empirically demonstrate that our proposed KBPT systematically yields improved revenue compared with model-based and data-driven benchmarks over various different assets.

Forecasting Financial Time Series (FTS) has been of interest to financial market participants who are interested in making profitable trades on the financial markets. It has historically been approached using stochastic and machine learning models. Stochastic methods include linear models such as Autoregressive Integrated Moving Average (ARIMA) [1] that support non-stationary time series and non-linear models, including the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) [2] model. Machine learning methods are data-driven approaches, among which Recurrent Neural Networks (RNNs) [3], more specifically, Long Short-Term Memory (LSTM) networks [4], have been especially popular for time series prediction. Periodically, new deep learning models are being adopted in quantitative research to find the most accurate models in FTS forecasting that would lead to more efficient trading strategies. Recently, a new type of deep learning [5] architecture called Transformer [6], relying on Attention [7], was introduced for Natural Language Processing (NLP) applications. Transformers have since been used in other applications such as computer vision tasks [8] and more recently in time series forecasting. This paper will focus on the application of Transformers in high-frequency FTS forecasting. FTS are characterized by properties including frequency, auto-correlation, heteroskedasticity, drift, and seasonality [9].

We present a new financial framework where two families of RL-based agents representing the Liquidity Providers and Liquidity Takers learn simultaneously to satisfy their objective. Thanks to a parametrized reward formulation and the use of Deep RL, each group learns a shared policy able to generalize and interpolate over a wide range of behaviors. This is a step towards a fully RL-based market simulator replicating complex market conditions particularly suited to study the dynamics of the financial market under various scenarios.

This article is a sequel to an article titled "A New Direction in AI -- Toward a Computational Theory of Perceptions," which appeared in the Spring 2001 issue of AI Magazine (volume 22, No. 1, 73-84). The concept of precisiated natural language (PNL) was briefly introduced in that article, and PNL was employed as a basis for computation with perceptions. In what follows, the conceptual structure of PNL is described in greater detail, and PNL's role in knowledge representation, deduction, and concept definition is outlined and illustrated by examples. What should be understood is that PNL is in its initial stages of development and that the exposition that follows is an outline of the basic ideas that underlie PNL rather than a definitive theory. A natural language is basically a system for describing perceptions. Perceptions, such as perceptions of distance, height, weight, color, temperature, similarity, likelihood, relevance, and most other attributes of physical and mental objects are intrinsically imprecise, reflecting the bounded ability of sensory organs, and ultimately the brain, to resolve detail and store information.

Then, a PLDA model is trained to measure thesimilarity of i-vectors. Replacing traditional i-vectors with speaker embedding models based on deep neural networks haslead to improvement in SV [4, 3]. Nonetheless, a PLDA classifier is still needed to compare the similarity of embeddings. More recently, end-to-end training of an embedding networkthat makes decision by comparing distance in the embedding to a cross-validated threshold outperformed traditional methods. For detailed comparison between embedding networksand i-vector based methods, we refer the reader to [6, 4, 3]. Building on top of these studies, our work focuses on the comparison between two different approaches for deep metric learning (TL [5, 6, 7, 8] and PNL [10]) for end-to-end speaker embedding models. Deep metric learning: End-to-end speaker embedding models can be seen as a form of deep metric learning, which has been widely studied in the machine learning literature. Early examples of metric learning with neural networks include signature[11] and face verification [12]. Both compare pairs of examples with standard similarity functions (e.g.

This article is a sequel to an article titled "A New Direction in AI--Toward a Computational Theory of Perceptions," which appeared in the Spring 2001 issue of AI Magazine (volume 22, No. 1, 73-84). The concept of precisiated natural language (PNL) was briefly introduced in that article, and PNL was employed as a basis for computation with perceptions. In what follows, the conceptual structure of PNL is described in greater detail, and PNL's role in knowledge representation, deduction, and concept definition is outlined and illustrated by examples. What should be understood is that PNL is in its initial stages of development and that the exposition that follows is an outline of the basic ideas that underlie PNL rather than a definitive theory. A natural language is basically a system for describing perceptions.