Admission control governs Quality of Service (QoS) in cognitive IoT networks (CIoTNs) in which secondary nodes opportunistically share spectrum with preemptive primary users. The optimal policy is of threshold type, but the threshold table is indexed by the 2N fully occupied channel configurations, so both model-free learning and on-chain enforcement scale poorly in N. We show that this table has low intrinsic complexity: across 55 randomised continuous-time Markov decision process (CTMDP) instances, a monotone step function of the aggregate secondary-user drain rate σ(n) carrying only 1.6–2.3 distinct levels reproduces 81–87% of the 2N table entries exactly, the remainder erring by a single queue slot. We give a quasi-static argument for why σ(n) is the right scalar summary. Using this regularity as an inductive bias, an index-pooled Q-learning read-out reduces discounted policy-value loss by up to 4.4× (1.55% to 0.36% at N=4, six seeds) at the largest sample budget, but adds variance and was worse than the per-configuration baseline in one of eight cells; we therefore also specify a deployment gate and report it as untested. We further report a negative result: projecting learned value differences onto the concave cone guaranteed by the structural theorem is inert at N=4 and yields at most a 0.22 percentage-point gain at N=3, because recovery is limited by configuration coverage rather than by shape violation. Finally, we implement Service Level Agreement (SLA) enforcement as a Solidity contract and measure it on a local Ethereum Virtual Machine. Index compression cuts policy-installation gas by 241.8× at N=16 (48.79M to 0.20M gas) and keeps installation in one transaction, but raises the per-decision cost by 14.4–18.4k gas; it is therefore a feasibility mechanism for large N and for frequently re-committed policies, not a uniform improvement.
For a single event with finitely many mutually exclusive outcomes, the full Kelly problem is to maximize expected log wealth over nonnegative stakes together with an optional cash position. The optimal formula is classical, but the support-selection step is often presented via Lagrange multipliers. This note gives a shorter state-price derivation. A cash fraction $c$ acts as an implicit position in every outcome: in terminal-wealth terms, it is equivalent to a baseline stake $cq_i$ on outcome $i$, where $q_i$ is the state price. On any active support, explicit bets therefore only top up favorable outcomes from this baseline $cq_i$ to the optimal total stake $p_i$. This yields the formula $x_i = (p_i - c q_i)_+$, the threshold rule $p_i/q_i > c$, and, after sorting outcomes by $p_i/q_i$, a one-pass greedy algorithm for support selection. The result is standard in substance, but the implicit-position viewpoint gives a compact proof and a convenient way to remember the solution.
This paper proposes an AI-based trading framework that integrates supervised price forecasting with reinforcement learning (RL)-based decision-making. The objective is to enhance both profitability and risk management in cryptocurrency trading by equipping RL agents with forward-looking market information and risk-aware incentives. The proposed methodology follows a two-stage design. First, a univariate long short-term memory (LSTM) model generates 72 bitcoin price forecasts. These predictions are used to compute future technical indicators, which are combined with current market indicators to construct an enriched, forward-looking state representation. Second, an RL agent is trained in this environment using a novel long-term reward function that incorporates transaction costs, drawdown penalties, volatility penalties, and delayed rewards to promote stable and sustainable trading behavior. Four state-of-the-art RL algorithms (PPO, SAC, TD3, and A2C) are systematically evaluated over randomized 180-day episodes using hourly bitcoin data. The results demonstrate that the proposed agent consistently outperforms conventional buy-and-hold and moving average crossover strategies, achieving an average profit ratio of 32% and a Sharpe ratio of 1.34. These findings highlight the novelty and effectiveness of combining mid-term price forecasts, enriched technical states, and risk-aware RL training for robust cryptocurrency trading.
Kwestan Ahmed Ismael, Heshu Othman Faqe, Mohammed Hussein Abdalla, Hindreen A. Taher
In this work we use historical market data from Bitget to predict weekly open prices of Ethereum (ETH) for a 96-week period with the Prophet forecast model trained by using Particle Swarm Optimization (PSO) algorithm. Because of this, the research delves into automated hyperparameter tuning for Prophet in order to improve forecast performance on cryptocurrency markets where volatility, structural breaks and irregular trading patterns pose a significant challenge to time series prediction. The PSO algorithm is a good method to explore the high dimensional parameter space in which it can strike between the global analysis and local exploitation for detecting minimal forecast errors. Based on evaluating model performance for which we used accuracy metrics such as Mean Squared Error (MSE), Root Mean Squared Error (RMSE), Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) in training, test holdout & full-fit situations. PSO-optimized Prophet: The results show a great in-sample fitting and fast convergence behaviour, as the best CV RMSE is slightly higher than the lowest one should have obtained if used only 10 iterations. Although forecasts exhibit stability and track long-term trends well, the model does not predict short-term fluctuations in the holdout set with high accuracy (wider forecast uncertainty intervals). Our results shed light on the utility of PSO to improve Prophet-based price prediction in cryptocurrencies, reinforce the relevance of uncertainty quantification in asset markets and inform risk-aware decisions of financial agents dealing with unstable assets.
Mohsen Minaei, Ranjit Kumaresan, Andrew Beams, Pedro Moreno-Sánchez · 9 authors
Blockchain auction plays an important role in the price discovery of digital assets (e.g.NFTs).However, despite their importance, implementing auctions directly on blockchains such as Ethereum incurs scalability issues.In particular, the on-chain transactions scale poorly with the number of bidders, leading to network congestion, increased transaction fees, and slower transaction confirmation time.This lack of scalability significantly hampers the ability of the system to handle largescale, high-speed auctions that are common in today's economy.In this work, we build a protocol where an auctioneer can conduct sealed bid auctions that run entirely off-chain when parties behave honestly, and in the event that k bidders deviate (e.g., do not open their sealed bid) from an n-party auction protocol, then the on-chain complexity is only O(k).This improves over existing solutions that require O(n) on-chain complexity, even if a single bidder deviates from the protocol.In the event of a malicious auctioneer, our protocol still guarantees that the auction will successfully terminate.We implement our protocol and show that it offers significant efficiency improvements compared to existing on-chain solutions.Our use of zkSnark to achieve scalability also ensures that the on-chain contract and other participants do not learn anything about the bidders' identities and their respective bids, except for the winner and the winning bid amount.
In this paper, I prove that sublinear regret across the environment Class C requires six functional properties, that these properties are mutually independent, and that they compose into a directed informational chain closing back on itself — a six-link cycle whose final link is grounded in an explicit Doob martingale construction over cycles of play. All six properties are defined functionally — as conditions on the distributions a decision-maker induces over actions and canonical summaries — so the results are invariant under implementation and apply to any decision-making system that can be modelled within the class: a person, an institution, or a machine. Every theorem in this paper, without exception, is checked line by line in the Lean 4 proof assistant against Mathlib: the formalization (~12,700 lines) contains zero `sorry`, zero custom axioms, and zero opaque definitions. Class C is the union of all POMDPs satisfying at least one of six structural properties covering the fundamental qualitative dimensions of adaptive hardness: reward ambiguity (P1), absorbing traps (P2), local optima (P3), deterministic optimality (P4), constrained feasibility (P5), and nonstationarity (P6). * Part I (Necessity). I define six primitives X1–X6 as purely functional properties of decision rules: Objective Tracking, Cross-Context Safety Transfer, Global Attractor Exploration, Policy Simplification, Feasibility Projection, and Feedback Adaptation. For each, I construct an explicit environment in C and prove an unconditional Ω(T) regret lower bound for any decision-maker lacking that primitive.* Part II (Independence). For every ordered pair (i,j) with i≠j, I exhibit an explicit decision rule possessing Xj but lacking Xi that suffers Ω(T) regret on the matching environment. All thirty directed-pair results are shown to follow from one master theorem, verified on a single compound environment with full non-interference analysis.* Part III (Sequential Dependence). Necessity is domain-invariant — a structural failure is a structural failure no matter what "success" means to the decision-maker — which is why Parts I and II hold unconditionally. Sufficiency is not: what counts as success is supplied by the domain, not by the theorem, so a single closed-form sufficiency result covering every domain at once would have to either fix one arbitrary notion of success and stop being general, or say nothing of substance. Part III proves exactly what generalizes. I prove six Information Enhancement Theorems establishing that the six primitives compose into a directed information chain: possessing Xi strictly increases the mutual information available toward any goal variable at Xi+1's task. Each of the six links is established outright — a forward theorem, a reverse theorem, and a non-reversibility result — with the exact point where a domain's own definition of success enters the chain named explicitly, as an Implementation Obligation, rather than assumed away. The closing link, X6→X1, is grounded in an actual Doob martingale construction: given that the cycle-indexed posterior is a martingale, it converges almost surely to the truth across cycles — the precise sense in which the chain accumulates rather than resets. To this paper's knowledge, no prior formalization unifies this many independently-proven-necessary structural properties into a single machine-checked class with proven mutual independence across all of them. All mathematical work is provided in full transparency and independent verification is highly encouraged: the complete Lean formalization, with a passing build and every theorem cross-referenced to its exact identifier, is at github.com/M-Ismail-ZA/IsmailsPrimitives. For any feedback or collaboration, please contact me via the email address listed on the paper. Updated: 3 July 2026 (V6.1).
Mohak Goyal, Geoffrey Ramseyer, Ashish Goel, David Mazières
Constant Function Market Makers (CFMMs) are a tool for creating exchange markets, have been deployed effectively in prediction markets, and are now especially prominent in the Decentralized Finance ecosystem. We show that for any set of beliefs about future asset prices, an optimal CFMM trading function exists that maximizes the fraction of trades that a CFMM can settle. We formulate a convex program to compute this optimal trading function. This program, therefore, gives a tractable framework for market-makers to compile their belief function on the future prices of the underlying assets into the trading function of a maximally capital-efficient CFMM. Our convex optimization framework further extends to capture the tradeoffs between fee revenue, arbitrage loss, and opportunity costs of liquidity providers. Analyzing the program shows how the consideration of profit and loss leads to a qualitatively different optimal trading function. Our model additionally explains the diversity of CFMM designs that appear in practice. We show that careful analysis of our convex program enables inference of a market-maker's beliefs about future asset prices, and show that these beliefs mirror the folklore intuition for several widely used CFMMs. Developing the program requires a new notion of the liquidity of a CFMM, and the core technical challenge is in the analysis of the KKT conditions of an optimization over an infinite-dimensional Banach space.
Abstract Deep reinforcement learning is gaining popularity in many different fields. An interesting sector is related to the definition of dynamic decision-making systems. A possible example is dynamic portfolio optimization, where an agent has to continuously reallocate an amount of fund into a number of different financial assets with the final goal of maximizing return and minimizing risk. In this work, a novel deep Q-learning portfolio management framework is proposed. The framework is composed by two elements: a set of local agents that learn assets behaviours and a global agent that describes the global reward function. The framework is tested on a crypto portfolio composed by four cryptocurrencies. Based on our results, the deep reinforcement portfolio management framework has proven to be a promising approach for dynamic portfolio optimization.
Hyperparameters are pivotal for machine learning models. The success of efficient calibration, often surpasses the results obtained by devising new approaches. Traditionally, human intervention is required to tune the models, however, this obtuse outlook restricts the proficiency and competence. Automating this crucial characteristic of learning sustainably, proffers a significant boost in performance and cost optimization. Blockchain technology has revolutionized industries utilizing its Proof-of-Work algorithms for consensus. This complicated solution generates a lot of useless computations across the nodes attached to the network and thus, fritters away a huge amount of precious energy. In this paper, we propose to exploit these inane computations for training deep learning models instead of calculating purposeless hash values, thus, suggesting a new consensus schema. This work distinguishes itself from other related works by capitalizing on the parallel processing prospects it generates for hyperparameter tuning of complex deep learning models. We address this aspect through the framework of Bayesian optimization which is an effective methodology for the global optimization of functions with expensive evaluations. We call our work, Proof of Deep Learning with Hyperparameter Optimization (PoDLwHO).
Automated market makers, first popularized by Hanson's logarithmic market scoring rule (or LMSR) for prediction markets, have become important building blocks, called 'primitives,' for decentralized finance. A particularly useful primitive is the ability to measure the price of an asset, a problem often known as the pricing oracle problem. In this paper, we focus on the analysis of a very large class of automated market makers, called constant function market makers (or CFMMs) which includes existing popular market makers such as Uniswap, Balancer, and Curve, whose yearly transaction volume totals to billions of dollars. We give sufficient conditions such that, under fairly general assumptions, agents who interact with these constant function market makers are incentivized to correctly report the price of an asset and that they can do so in a computationally efficient way. We also derive several other useful properties that were previously not known. These include lower bounds on the total value of assets held by CFMMs and lower bounds guaranteeing that no agent can, by any set of trades, drain the reserves of assets held by a given CFMM.
The focus of this thesis is twofold: on one hand we study the query complexity of equilibrium computation in games, and on the other hand, we use equilibrium concepts from game theory as a tool to understand miner incentives in Bitcoin. In terms of query complexity, we mostly focus on algorithms that have access to utility queries in large games and best response queries in bimatrix games. For the former, we demonstrate query-efficient completely uncoupled dynamics that achieve non-trivial approximate equilibria. For the latter, we reduce the problem of query-efficient approximate equilibrium computation to a natural geometric learning problem: approximately learning partitions of an 𝑛-dimensional simplex into disjoint convex polytopes via membership queries. Given this reduction we show query-efficient algorithms for the geometric problem, and ultimately provide an algorithm for computing e-well-supported Nash equilibria in 𝑚×𝑛 bimatrix games with a query cost that is polynomial in log(1/e)and max(𝑚,𝑛) provided that min(𝑚,𝑛) is constant.This leads to a polynomial query complexity algorithm for 2-player games,provided that one of the players has a constant number of strategies. As for incentives in Bitcoin, we shed some light into how robust honest mining protocols are to the presence of strategic agents. Our focus is on the strategic aspects of both solo mining and pool mining in Bitcoin. For the former, we take a multiplayer approach and exhibit specific strategy profiles of multiple strategic miners that outperform honest mining, even if said miners would not be incentivised to be dishonest individually. This effectively renders the Bitcoin protocol less secure than previously thought. As for the latter, we propose a new mining pool protocol that is a randomised variant of the already-ubiquitous pay-per-last-N-shares (PPLNS) mining pool scheme in Bitcoin. Our pool protocol, randomised pay-per-last-N-shares (RPPLNS),enjoys the same desirable properties of PPLNS, but with the added benefit of an exponentially reduced state space required to maintain the protocol. More importantly, this reduced state space also allows us to prove robust guarantees against a richer class of strategic pool mining than before.
Portfolio management is the decision-making process of allocating an amount of fund into different financial investment products. Cryptocurrencies are electronic and decentralized alternatives to government-issued money, with Bitcoin as the best-known example of a cryptocurrency. This paper presents a model-less convolutional neural network with historic prices of a set of financial assets as its input, outputting portfolio weights of the set. The network is trained with 0.7 years' price data from a cryptocurrency exchange. The training is done in a reinforcement manner, maximizing the accumulative return, which is regarded as the reward function of the network. Back test trading experiments with trading period of 30 minutes is conducted in the same market, achieving 10-fold returns in 1.8 month's periods. Some recently published portfolio selection strategies are also used to perform the same back tests, whose results are compared with the neural network. The network is not limited to cryptocurrency, but can be applied to any other financial markets.
The minmax regret problem for combinatorial optimization under uncertainty\ncan be viewed as a zero-sum game played between an optimizing player and an\nadversary, where the optimizing player selects a solution and the adversary\nselects costs with the intention of maximizing the regret of the player. The\nexisting minmax regret model considers only deterministic solutions/strategies,\nand minmax regret versions of most polynomial solvable problems are NP-hard. In\nthis paper, we consider a randomized model where the optimizing player selects\na probability distribution (corresponding to a mixed strategy) over solutions\nand the adversary selects costs with knowledge of the player's distribution,\nbut not its realization. We show that under this randomized model, the minmax\nregret version of any polynomial solvable combinatorial problem becomes\npolynomial solvable. This holds true for both the interval and discrete\nscenario representations of uncertainty. Using the randomized model, we show\nnew proofs of existing approximation algorithms for the deterministic model\nbased on primal-dual approaches. Finally, we prove that minmax regret problems\nare NP-hard under general convex uncertainty.\n