Improved Arbitrage Detection Algorithm

• The paper introduces a novel GNN and deep Q-learning hybrid that achieves a 6.3% yield with reduced latency compared to LP and Bellman-Ford methods.
• It integrates quantum annealing with classical post-processing to efficiently optimize currency cycle detection, achieving near-optimal profit in linear time.
• Additionally, the approach derives closed-form, GPU-scalable solutions for AMM arbitrage, enabling on-chain execution with orders-of-magnitude speed improvements.

An improved algorithm for identifying arbitrage opportunities aims to maximize the efficient and robust discovery of riskless profits in financial markets, addressing computational bottlenecks, coverage limitations, or practical deployment challenges of prior approaches. Contemporary research builds on various theoretical frameworks—graph theory, convex and combinatorial optimization, quantum and classical metaheuristics, and deep learning—each offering distinct advances in arbitrage opportunity identification across spot, derivative, currency, and decentralized markets.

1. Graph-Based and Deep Learning Methods for Currency Arbitrage

Classical triangular arbitrage detection relies on exhaustive search (e.g., Bellman-Ford cycles) or linear programming, resulting in high computational cost and limited scalability in real-time multi-currency environments. The approach in "Efficient Triangular Arbitrage Detection via Graph Neural Networks" (Zhang, 5 Feb 2025) recasts the currency market as a directed weighted graph, with nodes representing currencies and weighted edges representing exchange rates. A graph neural network (GNN) architecture is instantiated over this graph, propagating information via message passing:

$$\mathbf{h}_i^{(l+1)} = \sigma\left(\mathbf{W}^{(l)} \mathbf{h}_i^{(l)} + \sum_{j \in \mathcal{N}(i)} \mathbf{W}^{(l)} \mathbf{h}_j^{(l)} \cdot \mathbf{e}_{ij}\right)$$

where $\mathbf{h}_i^{(l)}$ encodes the latent state of currency $i$ at layer $l$, and $\mathbf{e}_{ij}$ encodes the exchange rate from $i$ to $j$. The GNN outputs actionable trade allocations $\mathbf{x}$. The conventional LP constraints enforcing flow-conservation are softened into a differentiable loss function:

$$\mathcal{L}(\mathbf{x}) = \left(\sum_{i,j} r_{ij} x_{ij} - \sum_{i,j} x_{ij}\right) - \lambda \sum_i \left(\sum_j x_{ij} - \sum_k r_{ki} x_{ki}\right)^2$$

This enables gradient-based learning that is computationally superior in dynamic settings. A further innovation is the integration of Deep Q-Learning principles: the GNN is trained to maximize expected arbitrage return over sequences, allowing generalization to unseen arbitrage cycles. Experimentally, this yields superior yield (6.3% vs. 6.0% for LP, 5.8% for Bellman-Ford) and much lower inference time (147 ms vs. 215–320 ms) on synthetic multi-asset data, making the method practical for high-frequency trading platforms.

2. Quantum and Hybrid Approaches to Currency Arbitrage

Quantum optimization is explored in papers such as (Deshpande et al., 8 Feb 2025, Roy et al., 11 Sep 2025), and (Carrascal et al., 2023), where currency arbitrage is reformulated as a binary (combinatorial) optimization to identify optimal currency cycles:

$\min \sum_{(i,j)} -\log(r_{ij})\, b_{ij}$

subject to constraints that enforce valid cycles (e.g., unique in/out edges per currency, simple cycle preservation). This can be encoded as QUBO/Ising Hamiltonians for quantum annealing (D-Wave) or further reduced for variational quantum algorithms (ACE, VQE, QAOA). Hybrid methods post-process quantum solutions using classical multi-bit swap local search for improved feasibility and profit.

Below is a comparative summary of recent benchmarks (Roy et al., 11 Sep 2025) for cycles across 14 currencies:

Solver	Cycle Size (Vars)	Profit (pips)	Time Scaling	Notes
D-Wave QA	up to 154	Optimal/similar	Linearize with size	Fast execution, hardware noise ignored
ACE-LS (sim)	up to 154	Near-optimal	Linear via qubit reduction	Needs classical post-processing
Gurobi (classical)	up to 154	Optimal	Exponential (size $\uparrow$)	Becomes impractical for $K>6$
Tabu Search	up to 154	Good	Linear	Heuristic, variable quality

Quantum methods currently match or closely approach classical optimality for small-to-medium graphs, with significant speed and clear advantages as problem size grows—though real quantum hardware with noise and connectivity constraints remains a challenge.

3. Closed-Form and Parallelizable Solutions for AMM Arbitrage

For decentralized exchanges, arbitrage in $N$-token automated market makers (AMMs, e.g., Balancer-like G3Ms) has traditionally required convex optimization. "Closed-form solutions for generic N-token AMM arbitrage" (Willetts et al., 9 Feb 2024) advances this by deriving analytical expressions for the optimal arbitrage trade vector $\Phi^*$ under the G3M invariant:

$$\prod_{i\in\mathcal{A}} \left(1 + \frac{\gamma^{d_i} \Phi_i}{R_i}\right)^{\breve{w}_i} = 1$$

where $\gamma$ models fees, $R_i$ is reserve, and $\breve{w}_i$ is normalized weight. The optimal solution for each active token $i$ is given by an explicit formula involving reserves, weights, fee scaling, and market prices, allowing the computation of all candidate arbitrage signatures $(s_i)$ in parallel on CPU or GPU. In practice, this closed-form:

• Outperforms convex solvers in both speed (orders of magnitude faster for $N \lesssim 7$) and often in arbitrage depth found,
• Is inherently parallel and GPU-scalable,
• Enables practical on-chain execution by dramatically reducing resource requirements,
• Shows, via simulation and backtests (e.g., ETH-BTC-DAI pool), superiority in "time-to-arb" metrics over legacy approaches.

4. Enhanced Detection in Decentralized and Prediction Markets

Recent progress in DEX arbitrage detection includes the use of line graphs and Modified Moore-Bellman-Ford algorithms (MMBF) (Zhang et al., 24 Jun 2024) to overcome the limitations of MBF, which only finds a narrow subset of cycles (arbitrage loops) and fails to enumerate non-loop arbitrage. The improved approach:

• Constructs the line graph $L(G)$ whose nodes represent edges in the DEX token swap network,
• Augments it with a source node to facilitate loop and non-loop path detection from any starting token,
• Executes an MMBF algorithm to uncover all profitable cycles and non-loop arbitrage paths.

Empirical studies on Uniswap V2 show this method detects orders of magnitude more opportunities, with much larger maximal profit (>$1M on some days vs. MBF's$\sim$$100K$$), and recovers both short and longer arbitrage paths. The method requires 8–10 seconds per 100-token DEX snapshot.</p> <p>In prediction markets, scalable arbitrage detection across thousands of markets and conditions is achieved by combining topical and temporal filtering, language-model-based dependency mapping, and outcome table analysis (<a href="/papers/2508.03474" title="" rel="nofollow" data-turbo="false" class="assistant-link" x-data x-tooltip.raw="">Saguillo et al., 5 Aug 2025</a>). This enables the identification of multi-market combinatorial arbitrage in platforms such as Polymarket, substantiated by heuristics and historical extraction analysis ($$>$$40M$$USD of profit detected).</p> <h2 class='paper-heading' id='statistical-arbitrage-high-dimensional-model-free-and-machine-learning-approaches'>5. Statistical Arbitrage: High-Dimensional, Model-Free, and Machine Learning Approaches</h2> <p>Advances in statistical arbitrage now include fully data-driven, model-free methods using deep neural networks (DNNs) and graph learning architectures. Notable methods (<a href="/papers/2203.03179" title="" rel="nofollow" data-turbo="false" class="assistant-link" x-data x-tooltip.raw="">Neufeld et al., 2022</a>, <a href="/papers/2510.10599" title="" rel="nofollow" data-turbo="false" class="assistant-link" x-data x-tooltip.raw="">Yadav et al., 12 Oct 2025</a>, <a href="/papers/2510.11616" title="" rel="nofollow" data-turbo="false" class="assistant-link" x-data x-tooltip.raw="">Epstein et al., 13 Oct 2025</a>, <a href="/papers/2406.10695" title="" rel="nofollow" data-turbo="false" class="assistant-link" x-data x-tooltip.raw="">Korniejczuk et al., 15 Jun 2024</a>, <a href="/papers/2508.14762" title="" rel="nofollow" data-turbo="false" class="assistant-link" x-data x-tooltip.raw="">Hong et al., 20 Aug 2025</a>) feature:</p> <ul> <li>DNNs parameterize trading strategies directly in high dimensions, eschewing reliance on cointegration, mean-reverting pairs, or fixed parametric dependence.</li> <li>Robustness to model ambiguity via Wasserstein-ball ambiguity sets and empirical measures, conditioning on all plausible market path perturbations (robust statistical arbitrage).</li> <li>Graph-based clustering (SPONGE$$_\text{sym}$$) and ensemble ML filtering, enhancing signal quality and reducing false positives, with risk-weighted Kelly sizing for optimal capital allocation (<a href="/papers/2406.10695" title="" rel="nofollow" data-turbo="false" class="assistant-link" x-data x-tooltip.raw="">Korniejczuk et al., 15 Jun 2024</a>).</li> <li>Synthetic long-short-arbitrage (SLSA) positions in options markets, constructed to be risk-minimal and Black-Scholes-neutral, informed by dedicated graph learning (e.g., RNConv architectures) on arbitrage-specific targets (<a href="/papers/2508.14762" title="" rel="nofollow" data-turbo="false" class="assistant-link" x-data x-tooltip.raw="">Hong et al., 20 Aug 2025</a>).</li> <li>End-to-end attention-based factor learning and sequence modeling (LongConv), directly optimizing net Sharpe ratio under trading frictions, and demonstrating strong out-of-sample risk-adjusted returns (Sharpe$$>$ 2.3 net) (Epstein et al., 13 Oct 2025).

For detection of model-free static arbitrage in high-dimensional options markets, it is proven (Neufeld et al., 2023) that a single neural network can approximate the entire arbitrage detection functional, mapping option surfaces to quadratic/semi-infinite feasibility problems, and yielding almost immediate detection and construction of optimal portfolios.

6. Enhanced Arbitrage Detection in Multi-Asset Derivative Markets

Multi-asset arbitrage is rigorously addressed by mapping the existence of arbitrage to the existence of an equivalent martingale measure (EMM) consistent with marginal risk-neutral distributions and multi-asset derivative prices (Papapantoleon et al., 2020). By invoking improved Fréchet-Hoeffding bounds—tightened for side constraints such as derivative prices or copula functionals—arbitrage is reduced to checking non-emptiness of a multi-constraint copula intersection via an explicit optimization:

$\min_{u \in [0,1]^d} \overline{Q}_{\mathbf{p}}(u) - \underline{Q}_{\mathbf{p}}(u)$

If the minimum is negative, joint arbitrage exists even if each derivative is individually priced within no-arbitrage bounds. This framework enables efficient numerical detection of joint arbitrage risk in complex derivatives portfolios.

7. Practical Impact, Deployment, and Future Directions

These improved algorithms exhibit significant advances in computational performance (e.g., reduced latency, linear time scaling for quantum/classical hybrids), opportunity coverage (e.g., all arbitrage cycles and non-loops, multi-asset portfolios), and practical deployability under real-time constraints and market frictions.

Key implementation takeaways:

• Embarrassingly parallel and closed-form methods are preferred for on-chain and real-time contexts,
• GNN- and ML-based methods rapidly adapt to high-dimensional, dynamic, structurally complex markets,
• Quantum and post-processing hybrid approaches offer a path to scale as hardware matures,
• Robustness to parameter/tuning variations and transaction costs is critical for sustained outperformance.

The field continues to evolve towards more scalable, learning-based, and robust frameworks for arbitrage detection and exploitation in increasingly fragmented, diverse, and rapid financial markets.